Edgar Filing: PIONEER MUNICIPAL HIGH INCOME TRUST

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                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM N-Q

                   CERTIFIED SHAREHOLDER REPORT OF REGISTERED
                        MANAGEMENT INVESTMENT COMPANIES



  Investment Company Act file number 811-21321


                    Pioneer Municipal High Income Trust
               (Exact name of registrant as specified in charter)


                       60 State Street, Boston, MA 02109
              (Address of principal executive offices) (ZIP code)


            Terrence J Cullen, Pioneer Investment Management, Inc.,
                       60 State Street, Boston, MA 02109
                    (Name and address of agent for service)


Registrant's telephone number, including area code:  (617) 742-7825


Date of fiscal year end:  April 30

Date of reporting period:  January 31, 2012

Form N-Q is to be used by management investment companies, other than small
business investment companies registered on Form N-5 (239.24 and 274.5 of this
chapter), to file reports with the Commission, not later than 60 days after
close of the first and third fiscal quarters, pursuant to Rule 30b1-5under
the Investment Company Act of 1940 (17 CFR 270.30b-5).  The Commission may
use the information provided on Form N-Q in its regulatory, disclosure review,
inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-Q,
and the Commission will make this information public. A registrant is not
required to respond to the collection of information contained in Form N-Q
unless the Form displays a currently valid Office of Management and Budget
("OMB") control number. Please direct comments concerning the accuracy of the
information collection burden estimate and any suggestions for reducing the
burden to Secretary, Securities and Exchange Commission, 450 Fifth Street, NW,
Washington, DC 20549-0609.  The OMB has reviewed this collection of information
under the clearance requirements of 44 U.S.C. ss. 3507.


<PAGE>
ITEM 1. Schedule of Investments.

Principal Amount USD $				S&P / Moody's Ratings				Value
						TAX-EXEMPT OBLIGATIONS — 127.0% of Net Assets
						Alabama — 2.2%
	2,500,000				B-/B2	Alabama Industrial Development Authority Solid Waste Disposal Revenue, 6.45%, 12/1/23	$		2,261,250
	1,000,000				NR/NR	Huntsville-Redstone Village Special Care Facilities Financing Authority, 5.5%, 1/1/28			925,950
	4,500,000				NR/NR	Huntsville-Redstone Village Special Care Facilities Financing Authority, 5.5%, 1/1/43			3,565,710

							$		6,752,910
						Arizona — 2.4%
	5,000,000				BBB-/Baa3	Apache County Industrial Development Authority, 5.85%, 3/1/28	$		5,001,800
	994,000				NR/Baa3	Pima County Industrial Development Authority, 6.75%, 7/1/31			994,398
	950,000				NR/Baa3	Pima County Industrial Development Authority, 7.25%, 7/1/31			952,175
	500,000				NR/Baa2	Yavapai County Industrial Development Authority, 6.0%, 8/1/33			508,005

							$		7,456,378
						California — 9.7%
	3,000,000				NR/A1	ABAG Finance Authority for Nonprofit Corp. Revenue Bonds, 5.75%, 7/1/37	$		3,155,250
	1,000,000				NR/NR	California Enterprise Development Authority Recovery Zone Facility Revenue, 8.5%, 4/1/31			1,064,650
	7,885,000		(a)		AA-/NR	California State University Revenue, RIB, 11.126%, 9/20/28 (144A)			9,595,178
	3,000,000				BB+/NR	California Statewide Communities Development Authority, 7.25%, 10/1/38 (144A)			3,112,410
	568,006		(b)		NR/NR	California Statewide Communities Development Authority Environmental Facilities Revenue, 9.0%, 12/1/38			5,504
	5,150,000		†		AA+/Aaa	Golden State Tobacco Securitization Corp., 7.8%, 6/1/42			5,651,713
	7,000,000		†		AA+/Aaa	Golden State Tobacco Securitization Corp., 7.875%, 6/1/42			7,688,590

							$		30,273,295
						Colorado — 1.0%
	2,000,000				BBB+/NR	Colorado Health Facilities Authority Revenue, 5.25%, 5/15/42	$		1,993,820
	1,000,000				NR/NR	Kremmling Memorial Hospital District, 7.125%, 12/1/45			1,055,510

							$		3,049,330
						Connecticut — 6.0%
	10,335,000		(a)		NR/Aaa	Connecticut Health & Educational Facilities Authority Revenue, RIB, 11.885%, 8/21/35 (144A)	$		13,715,475
	1,000,000				NR/NR	Hamden Facility Revenue Bonds, Series 2009A, 7.75%, 1/1/43			1,043,060
	5,000,000				CCC+/NR	Mohegan Tribe Indians Gaming Authority, 6.25%, 1/1/31			4,133,650

							$		18,892,185
						District Of Columbia — 3.7%
	5,000,000				BBB/Baa1	District of Columbia Tobacco Settlement Financing Corp., 6.5%, 5/15/33	$		5,417,800
	6,000,000				BBB/Baa1	District of Columbia Tobacco Settlement Financing Corp., 6.75%, 5/15/40			6,070,320

							$		11,488,120
						Florida — 7.6%
	1,500,000				NR/NR	Alachua County Health Facilities Authority Revenue, 8.125%, 11/15/41	$		1,520,685
	1,500,000				NR/NR	Alachua County Health Facilities Authority Revenue, 8.125%, 11/15/46			1,520,685
	1,600,000				NR/NR	Beacon Lakes Community Development, 6.9%, 5/1/35			1,626,656
	1,000,000				NR/Ba3	Capital Trust Agency Revenue Bonds, 7.75%, 1/1/41			1,049,710
	1,000,000				NR/NR	Florida Development Finance Corp., Educational Facilities Revenue, 6.0%, 9/15/40			1,016,050
	2,000,000				NR/NR	Florida Development Finance Corp., Educational Facilities Revenue, 7.625%, 6/15/41			2,095,400
	1,000,000				NR/NR	Florida Development Finance Corp., Educational Facilities Revenue, 7.75%, 6/15/42			1,025,430
	1,000,000		†		NR/WR	Hillsborough County Industrial Development Authority Revenue, 8.0%, 8/15/32			1,457,140
	2,330,000				NR/NR	Liberty County Subordinate Revenue, 8.25%, 7/1/28			2,334,707
	2,500,000				A-/A2	Miami-Dade County Florida Aviation Revenue, 5.5%, 10/1/41			2,769,725
	1,000,000				NR/NR	St. Johns County Industrial Development Authority Revenue, 5.25%, 1/1/26			849,060
	2,000,000				NR/NR	St. Johns County Industrial Development Authority Revenue, 5.375%, 1/1/40			1,526,840
	5,000,000				NR/Baa1	Tallahassee Health Facilities Revenue, 6.375%, 12/1/30			5,006,600

							$		23,798,688
						Georgia — 2.6%
	4,240,000		(a)		NR/Aa3	Atlanta Georgia Water and Wastewater Revenue, RIB, 11.126%, 1/30/13 (144A)	$		4,765,506
	500,000				CCC+/NR	Clayton County Development Authority Revenue, 9.0%, 6/1/35			536,845
	2,400,000				NR/NR	Fulton County Residential Care Facilities Revenue, 5.0%, 7/1/27			1,932,120
	1,100,000				NR/NR	Fulton County Residential Care Facilities Revenue, 5.125%, 7/1/42			792,429

							$		8,026,900
						Idaho — 1.6%
	5,000,000				BBB+/Baa1	Power County Industrial Development Corp., 6.45%, 8/1/32	$		5,005,800
						Illinois — 14.4%
	1,000,000		(b)		NR/NR	Illinois Finance Authority Revenue, 6.0%, 11/15/27	$		500,000
	3,865,000				BBB+/NR	Illinois Finance Authority Revenue, 6.0%, 8/15/38			4,134,004
	2,000,000				AA+/Aa2	Illinois Finance Authority Revenue, 6.0%, 8/15/39			2,300,180
	4,000,000		(b)		NR/NR	Illinois Finance Authority Revenue, 6.0%, 11/15/39			2,000,000
	2,450,000				NR/NR	Illinois Finance Authority Revenue, 6.375%, 5/15/17			2,451,739
	2,500,000				NR/Baa2	Illinois Finance Authority Revenue, 6.5%, 4/1/39			2,724,225
	500,000				NR/NR	Illinois Finance Authority Revenue, 7.0%, 5/15/18			500,305
	1,700,000				NR/NR	Illinois Finance Authority Revenue, 7.625%, 5/15/25			1,717,340
	600,000				NR/NR	Illinois Finance Authority Revenue, 7.75%, 5/15/30			604,986
	2,000,000				NR/NR	Illinois Finance Authority Revenue, 8.0%, 5/15/40			2,018,860
	3,200,000				NR/NR	Illinois Finance Authority Revenue, 8.0%, 5/15/46			3,230,176
	4,000,000				NR/NR	Illinois Finance Authority Revenue, 8.25%, 5/15/45			4,032,520
	2,500,000				NR/NR	Illinois Finance Authority Revenue, 8.25%, 2/15/46			2,498,425
	16,880,000		(c)		AAA/A3	Metropolitan Pier & Exposition Authority Dedicated State Tax Revenue, 0.0%, 6/15/22			15,169,043
	1,540,000				NR/NR	Southwestern Illinois Development Authority Revenue, 5.625%, 11/1/26			1,153,368

							$		45,035,171
						Indiana — 2.0%
	3,000,000				A+/A1	Indiana Health & Educational Facility Financing Authority Hospital Revenue, 5.0%, 2/15/39	$		3,058,110
	3,570,000				NR/NR	Vigo County Hospital Authority Revenue, 5.8%, 9/1/47 (144A)			3,216,641

							$		6,274,751
						Louisiana — 2.1%
	1,500,000				BBB-/Baa3	Louisiana Local Government Environmental Facilities Revenue, 6.75%, 11/1/32	$		1,619,535
	5,000,000				NR/Baa1	Louisiana Public Facilities Authority Revenue, 5.5%, 5/15/47			5,106,850

							$		6,726,385
						Maine — 0.5%
	1,500,000				NR/Baa3	Maine Health & Higher Educational Facilities Authority Revenue, 7.5%, 7/1/32	$		1,718,115
						Massachusetts — 7.6%
	7,100,000				A/WR	Massachusetts Development Finance Agency, 5.75%, 1/1/42	$		8,712,907
	2,305,000				NR/NR	Massachusetts Development Finance Agency, 7.1%, 7/1/32			2,063,851
	860,000				AA/NR	Massachusetts Educational Financing Authority Revenue, 6.0%, 1/1/28			993,360
	1,860,000				AAA/Aaa	Massachusetts Health & Educational Facilities Authority Revenue, 5.5%, 7/1/32			2,680,613
	1,000,000				NR/Caa1	Massachusetts Health & Educational Facilities Authority Revenue, 6.0%, 10/1/23			776,810
	3,500,000		†		NR/NR	Massachusetts Health & Educational Facilities Authority Revenue, 6.25%, 7/1/22			3,620,680
	4,500,000		(b)		NR/NR	Massachusetts Health & Educational Facilities Authority Revenue, 6.5%, 1/15/38			44,955
	5,000,000				BB-/NR	Massachusetts Health & Educational Facilities Authority Revenue, 6.75%, 10/1/33			5,050,600

							$		23,943,776
						Michigan — 3.1%
	935,000				NR/NR	Doctor Charles Drew Academy, 5.7%, 11/1/36	$		632,855
	1,500,000				BB-/NR	John Tolfree Health System Corp., 6.0%, 9/15/23			1,320,975
	2,000,000				BB+/NR	Kent Hospital Finance Authority Revenue, 6.25%, 7/1/40			2,025,260
	5,830,000				B-/NR	Michigan Tobacco Settlement Finance Authority, 6.0%, 6/1/48			4,375,648
	1,410,000				BBB/NR	Star International Academy Certificates of Participation, 6.125%, 3/1/37			1,360,100

							$		9,714,838
						Minnesota — 0.9%
	1,675,000				BB-/NR	Duluth Economic Development Authority Health Care Facilities Revenue, 7.25%, 6/15/32	$		1,691,164
	1,000,000				NR/NR	Port Authority of the City of Bloomington Minnesota Facility Revenue Bonds, 9.0%, 12/1/35			1,064,690

							$		2,755,854
						Montana — 0.1%
	1,600,000		(b)(d)		NR/NR	Two Rivers Authority, Inc., Correctional Facility Improvement Revenue, 7.375%, 11/1/27	$		240,048
						Nebraska — 0.2%
	2,000,000		(b)(d)		NR/NR	Grand Island Solid Waste Disposal Facilities Revenue, 7.0%, 6/1/23	$		566,220
						Nevada — 0.0%*
	2,000,000		(b)(d)		NR/NR	Nevada State Department of Business & Industry, 7.25%, 1/1/23	$		2,400
						New Jersey — 7.9%
	10,000,000				B/B3	New Jersey Economic Development Authority Revenue, 6.25%, 9/15/29	$		9,956,900
	6,150,000		(e)		B/B3	New Jersey Economic Development Authority Revenue, 7.0%, 11/15/30			6,150,246
	8,000,000		†		AA+/Aaa	Tobacco Settlement Financing Corp., 6.75%, 6/1/39			8,693,600

							$		24,800,746
						New Mexico — 1.2%
	1,500,000				NR/NR	Otero County New Mexico Project Revenue, 6.0%, 4/1/23	$		1,337,385
	2,960,000				NR/NR	Otero County New Mexico Project Revenue, 6.0%, 4/1/28			2,451,146

							$		3,788,531
						New York — 10.1%
	2,000,000				NR/NR	Chautauqua County Capital Resource Corp. Revenue, 8.0%, 11/15/30	$		2,128,220
	3,000,000				NR/NR	Dutchess County Industrial Development Agency Revenue, 7.5%, 3/1/29			3,034,230
	2,000,000				BBB+/NR	Hempstead Local Development Corp. Revenue Bonds, 5.75%, 7/1/39			2,186,400
	2,050,000				NR/NR	Nassau County New York Industrial Development Agency Revenue, 6.7%, 1/1/43			1,592,092
	2,000,000				BB-/B2	New York City Industrial Development Agency, 5.25%, 12/1/32			1,616,240
	2,000,000				BB-/B2	New York City Industrial Development Agency, 7.625%, 12/1/32			2,001,200
	2,000,000				NR/C	New York City Industrial Development Agency, 8.0%, 8/1/12			1,843,640
	1,000,000				NR/Ba1	New York State Dormitory Authority Revenue, 6.125%, 12/1/29			1,024,080
	7,040,000		(a)		NR/Aaa	New York State Dormitory Authority Revenue, RIB, 13.432%, 5/29/14 (144A)			10,790,771
	2,750,000				BB/NR	Seneca Nation Indians Capital Improvement Authority Revenue, 5.25%, 12/1/16 (144A)			2,606,697
	3,000,000				NR/NR	Suffolk County Industrial Development Agency, 7.25%, 1/1/30			2,999,580

							$		31,823,150
						North Carolina — 2.9%
	4,785,000				NR/NR	Charlotte North Carolina Special Facilities Revenue, 5.6%, 7/1/27	$		4,171,228
	4,795,000				NR/NR	Charlotte North Carolina Special Facilities Revenue, 7.75%, 2/1/28			4,801,665

							$		8,972,893
						Oklahoma — 0.3%
	1,225,000		(b)		NR/NR	Tulsa Municipal Airport Revenue, 6.25%, 6/1/20	$		921,004
						Pennsylvania — 2.5%
	1,550,000				NR/Baa2	Allegheny County Hospital Development Authority Revenue, 5.125%, 5/1/25	$		1,550,186
	1,000,000				CC/NR	Columbia County Hospital Authority Health Care Revenue, 5.9%, 6/1/29			961,640
	665,000				BBB+/Baa3	Hazleton Health Services Authority Hospital Revenue, 5.625%, 7/1/17			665,499
	1,280,000		(b)		NR/NR	Langhorne Manor Borough Higher Education & Health Authority Revenue, 7.35%, 7/1/22			371,187
	5,000,000				B-/Caa2	Pennsylvania Economic Development Financing Authority Solid Waste Disposal Revenue, 6.0%, 6/1/31			3,939,500
	500,000				BBB+/NR	Pennsylvania Higher Educational Facilities Authority Revenue, 5.4%, 7/15/36			508,575

							$		7,996,587
						Rhode Island — 2.0%
	6,000,000		(d)		NR/NR	Central Falls Detention Facilities Revenue, 7.25%, 7/15/35	$		4,793,940
	1,500,000				NR/NR	Rhode Island Health & Educational Building Corp Revenue, 8.375%, 1/1/46			1,547,535

							$		6,341,475
						South Carolina — 1.3%
	3,185,000		†		BBB+/Baa1	South Carolina Jobs Economic Development Authority Revenue, 6.375%, 8/1/34	$		3,462,923
	665,000		†		BBB+/Baa1	South Carolina Jobs Economic Development Authority Revenue, 6.375%, 8/1/34			724,604

							$		4,187,527
						Tennessee — 4.7%
	7,000,000		†		NR/A2	Johnson City Health & Educational Facilities Board Hospital Revenue, 7.5%, 7/1/33	$		7,373,450
	2,480,000				NR/A1	Knox County Health, Educational & Housing Facilities Board Hospital Revenue, 6.375%, 4/15/22			2,536,222
	4,600,000				BBB+/NR	Sullivan County Health, Educational & Housing Facilities Board Hospital Revenue, 5.25%, 9/1/36			4,691,632

							$		14,601,304
						Texas — 14.6%
	1,345,000				NR/B3	Bexar County Housing Finance Corp., 8.0%, 12/1/36	$		949,395
	2,500,000				BB+/Ba1	Central Texas Regional Mobility Authority Revenue, 6.75%, 1/1/41			2,620,825
	4,000,000				NR/NR	Decatur Hospital Authority Revenue, 7.0%, 9/1/25			4,049,400
	725,078		(b)(d)		NR/NR	Gulf Coast Industrial Development Authority, 7.0%, 12/1/36			6,990
	3,750,000				B-/B3	Houston Airport System Special Facilities Revenue, 5.7%, 7/15/29			3,543,975
	5,340,000				NR/NR	Lubbock Health Facilities Development Corp., 6.625%, 7/1/36			5,240,249
	10,000,000				BBB+/A3	North Texas Tollway Authority Revenue, 5.75%, 1/1/33			10,908,000
	2,810,000		(a)		NR/Aaa	Northside Independent School District, RIB, 11.669%, 6/15/12 (144A)			3,159,705
	1,500,000				NR/NR	Red River Health Facilities Development Corp., Revenue, 8.0%, 11/15/41			1,536,480
	2,000,000				NR/NR	Tarrant County Cultural Education Facilities Finance Corp., 8.0%, 11/15/34			2,061,880
	1,000,000				NR/NR	Tarrant County Cultural Education Facilities Finance Corp., 8.125%, 11/15/39			1,023,370
	1,500,000				NR/NR	Tarrant County Cultural Education Facilities Finance Corp., 8.25%, 11/15/44			1,539,000
	7,040,000		(a)		NR/Aaa	Texas State, RIB, 12.64%, 4/1/13 (144A)			9,292,518

							$		45,931,787
						Vermont — 0.5%
	1,500,000				A-/Baa1	Vermont Educational & Health Buildings Financing Agency Revenue, 6.0%, 10/1/28	$		1,581,840
						Virginia — 0.3%
	1,000,000				BBB/Ba1	Peninsula Ports Authority, 6.0%, 4/1/33	$		1,027,090
						Washington — 9.9%
	4,710,000				A+/A2	Spokane Public Facilities District Hotel/Motel Tax & Sales, 5.75%, 12/1/27	$		5,040,454
	7,025,000				BBB/Baa1	Tobacco Settlement Authority Revenue, 6.625%, 6/1/32			7,307,194
	14,315,000				AA+/Aa1	Washington State General Obligation, 0.0%, 6/1/22			10,931,220
	3,795,000				A/A2	Washington State Health Care Facilities Authority Revenue, 6.0%, 1/1/33			4,175,525
	5,000,000				NR/NR	Washington State Housing Finance Committee Nonprofit Revenue, 5.625%, 1/1/27			3,635,400

							$		31,089,793
						West Virginia — 0.3%
	745,000				NR/NR	West Virginia Hospital Finance Authority Hospital Revenue Bonds, 9.125%, 10/1/41	$		826,808
						Wisconsin — 0.8%
	2,500,000				NR/NR	Wisconsin Public Finance Authority Continuing Care Retirement Community Revenue, 8.25%, 6/1/46	$		2,622,550
						TOTAL TAX-EXEMPT OBLIGATIONS (Cost $374,019,744)	$		398,234,249
						MUNICIPAL COLLATERALIZED DEBT OBLIGATION — 2.2% OF NET ASSETS
	10,000,000		(d)(e)		NR/NR	Non-Profit Preferred Funding Trust I, 6.75%, 9/15/37 (144A)	$		6,938,500
						TOTAL MUNICIPAL COLLATERALIZED DEBT OBLIGATION (Cost $10,000,000)	$		6,938,500
Shares								Value
						COMMON STOCK — 0.8%
						Transportation — 0.8%
	251,078		(f)			Delta Air Lines, Inc.	$		2,648,873

						TOTAL COMMON STOCKS (Cost $6,612,756)	$		2,648,873
						TOTAL INVESTMENTS IN SECURITIES — 130.0% (Cost $390,632,500)(g)(h)	$		407,821,622
						OTHER ASSETS AND LIABILITIES — 2.2%	$		6,757,926
						PREFERRED SHARES AT REDEMPTION VALUE, INCLUDING DIVIDENDS PAYABLE — (32.2)%	$		(101,001,172)
						NET ASSETS APPLICABLE TO COMMON SHAREOWNERS — 100.0%	$		313,578,376

(144A)		Security is exempt from registration under Rule 144A of the Securities Act of 1933. Such securities may be resold normally to qualified institutional buyers in a transaction exempt from registration. At January 31, 2012, the value of these securities amounted to $67,193,401 or 21.4% of total net assets applicable to common shareowners.
NR		Security not rated by S&P or Moody's
RIB		Residual Interest Bonds
WR		Withdrawn rating
†		Prerefunded bonds have been collateralized by U.S. Treasury or U.S. Government Agency securities which are held in escrow to pay interest and principal on the tax exempt issue and to retire the bonds in full at the earliest refunding date.
*		Amount rounds to less than 0.1%.
(a)		The interest rate is subject to change periodically and inversely based upon prevailing market rates. The interest rate shown is the coupon rate at January 31, 2012.
(b)		Security is in default and is non-income producing.
(c)		Debt obligation initially issued at one coupon which converts to a higher coupon at a specific date. The rate shown is the rate at January 31, 2012.
(d)		Indicates a security that has been deemed illiquid. The aggregate cost of illiquid securities is $22,082,721. The aggregate fair value of $12,548,098 represents 4.0% of the total net assets applicable to common shareowners.
(e)		The interest rate is subject to change periodically. The interest rate shown is the coupon rate at January 31, 2012.
(f)		Non-income producing.

	The concentration of investments by type of obligation/market sector is as follows:

Insured:
	NATL-RE	5.1	%
	FSA	3.6
	AMBAC	2.9
	NATL-RE FGIC	2.7
	PSF-GTD	0.8
Revenue Bonds:
	Medical Revenue	21.7
	Other Revenue	13.5
	Tobacco Revenue	11.3
	Health Revenue	9.9
	Development Revenue	7.3
	Education Revenue	6.2
	Airport Revenue	6.0
	Facilities Revenue	3.1
	Pollution Control Revenue	3.0
	Transportation Revenue	2.7
	Housing Revenue	0.2
	Utilities Revenue**	0.0
		100	%


Various inputs are used in determining the value of the Trust’s investments.
These inputs are summarized in the three broad levels listed below.

Level 1 – quoted prices in active markets for identical securities

Level 2 – other significant observable inputs (including quoted prices for similar securities,
interest rates, prepayment speeds, credit risk, etc.)

Level 3 – significant unobservable inputs (including the Trust’s own
assumptions in determining fair value of investments)

Generally, equity securities are categorized as Level 1, fixed income securities and senior loans
are categorized as Level 2 and securities valued using fair value
methods (other than prices supplied by independent pricing services) are categorized as Level 3.


	Level 1	Level 2	Level 3	Total
Tax exempt obligations	$—	$398,234,249	$—	$398,234,249
Municipal collateralized debt obligation	—	6,938,500	—	6,938,500
Common stocks	2,648,873	—	—	2,648,873
Total	$2,648,873	$405,172,749	$—	$407,821,622

ITEM 2. CONTROLS AND PROCEDURES. (a) Disclose the conclusions of the registrant's principal executive officer or officers and principal financial officer or officers, or persons performing similar functions, about the effectiveness of the registrant's disclosure controls and procedures (as defined in Rule 30a-3(c) under the Act (17 CFR 270.30a-3(c))) as of a date within 90 days of the filing date of the report that includes the disclosure required by this paragraph, based on their evaluation of these controls and procedures required by Rule 30a-3(b) under the Act (17 CFR270.30a-3(b))) and Rule 13a-15(b) or 15d-15(b) under the Exchange Act (17 CFR240.13a-15(b) or 240.15d-15(b)). The registrant's principal executive officer and principal financial officer have concluded that the registrant's disclosure controls and procedures are effective based on their evaluation of these controls and procedures as of a date within 90 days of the filing date of this report. (b) Disclose any change in the registrant's internal controls over financial reporting (as defined in Rule 30a-3(d) under the Act (17 CFR270.30a-3(d)) that occurred during the registrant's last fiscal quarter that has materially affected, or is reasonably likely to materially affect, the registrant's internal control over financial reporting. There were no significant changes in the registrant's internal control over financial reporting that occurred during the second fiscal quarter of the period covered by this report that have materially affected, or are reasonably likely to materially affect, the registrant's internal control over financial reporting. ITEM 3. EXHIBITS. (a) A separate certification for each principal executive officer and principal financial officer of the registrant as required by Rule 30a-2 under the Act (17 CFR 270.30a-2). Filed herewith. <PAGE> SIGNATURES [See General Instruction F] Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized. (Registrant) Pioneer Municipal High Income Trust By (Signature and Title)* /s/ John F. Cogan, Jr. John F. Cogan, Jr, President Date March 30, 2012 Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, this report has been signed below by the following persons on behalf of the registrant and in the capacities and on the dates indicated. By (Signature and Title)* /s/ John F. Cogan, Jr. John F. Cogan, Jr., President Date March 30, 2012 By (Signature and Title)* /s/ Mark Bradley Mark Bradley, Treasurer Date March 30, 2012 * Print the name and title of each signing officer under his or her signature.