Contract

EX-28.h.4

__________________, 2010

BRIDGEWAY FUNDS, INC.

Re:           Administration and Accounting and Transfer Agency Services Fee Waiver

Dear Sir or Madam:

PNC Global Investment Servicing (U.S.) Inc. (“PNC”) agrees to waive certain fees under (i) an Administration and Accounting Services Agreement dated December 30, 2009 and effective as of February 20, 2010 between Bridgeway Funds, Inc. (the “Fund”) and PNC and (ii) a Transfer Agency Services Agreement dated December 30, 2009 and effective as of February 20, 2010 between the Fund and PNC as set forth below. Each of the Administration and Accounting Services Agreement and Transfer Agency Services Agreement will be referred to herein as the “Agreement” and collectively, as the “Agreements.”

In order to assist in the successful launch of the Small-Cap Momentum Fund, PNC agrees to waive the following fees for a three-month period beginning ____________, 2010:

(A) For administration and accounting services PNC will waive 100% of the base fees, multiple class fee, multiple manager fee, data repository and analytics suite access fee, the portion of the regulatory administration services fees allocated to the Small-Cap Momentum Fund, and the taxation services fee. All other fees (i.e., asset based fees, portfolio reorganization fee, subadvisor change fee, financial typesetting fee, bank loan processing fee, independent security market quote costs, base 38a-1 compliance support service fee, and elective additional regulatory filing service fees) including out-of-pocket expenses will be billed as incurred.

(B) For transfer agency services PNC will waive 100% of the minimum monthly fee for the Small-Cap Momentum Fund during the aforementioned waiver period. All other fees (i.e., account fee, IRA custodian fee, transaction charges, PNC FundSERV networking fees, compliance fees, voice response fees, rule 22c-2 support services fees, print mail services fees, ancillary services fees) including miscellaneous charges, out-of-pocket expenses and shareholder expenses will be billed as incurred.

For clarity, this waiver applies solely to the Small-Cap Momentum Fund. Should the Small-Cap Momentum Fund cease operations prior to the end of the Initial Term of either Agreement, the Fund shall pay PNC an amount equal to 100% of the fees waived under such Agreement from the date hereof through the date of such termination.

PNC GLOBAL INVESTMENT SERVICING (U.S.) INC.

By:                _____________________

Name:           _____________________

Title:             _____________________

Agreed and Accepted:

BRIDGEWAY FUNDS, INC.

By:                ______________________

Name:           ______________________

Title:             ______________________