<PAGE>   1
(*) INFORMATION HAS BEEN OMITTED PURSUANT TO A REQUEST FOR CONFIDENTIAL
TREATMENT AND HAS BEEN FILED SEPARATELY WITH THE SECURITIES AND EXCHANGE
COMMISSION.

                                                                   EXHIBIT 10.16

                              AMENDMENT AGREEMENT

        This Amendment Agreement ("Amendment") is entered into as of June 30,
1999 by and between Inktomi Corporation, a Delaware corporation with its
principal place of business at 1900 South Norfolk Street, Suite 310, San Mateo,
California, 94403 ("Inktomi") and N2H2, Inc., a Washington corporation with its
principal place of business at 900 4th Avenue, Suite 3400, Seattle, Washington,
98164 ("N2H2").

                                    RECITALS

        A. Inktomi and N2H2 entered into a Search Engine Services Agreement
dated as of January 19, 1998 (the "Agreement")

        B. Inktomi and N2H2 wish to amend the Agreement as set forth herein.

                                    AGREEMENT

        In consideration of the foregoing and the mutual promises contained
herein, the parties agree as follows:

        1. Section 1.11 (Definition of Net Revenues) is hereby amended and
restated in its entirety to read as follows:

                "1.11 "Net Revenues" are gross advertising and sponsorship
        revenues booked by N2H2 attributable to (i) the search service operated
        by N2H2 through the Sites and (ii) all Initial Search Pages, all Results
        Pages and all other Web pages on the Sites that relate to the function
        of search provided by Inktomi, including without limitation save
        searches pages and Add URL pages (collectively the "Search Related
        Pages"), less: (a) fees actually payable by N2H2 to external third
        parties and direct internal sales expenses actually incurred by N2H2 for
        and relating to the placement of advertisements and sponsorships on the
        Search Related Pages (provided however that the external third party
        expenses shall be capped at *40% of gross revenue generated by N2H2
        relating to the placement of advertisements and sponsorships on the
        Search Related Pages and the direct internal sales expenses shall be
        capped at *20% of gross revenue generated by N2H2 relating to the
        placement of advertisements and sponsorships on the Search Related
        Pages); (b) taxes actually payable by N2H2 and not re-billed or
        re-billable to a third party (other than taxes based on N2H2's income),
        if any, attributable to the search services provided by N2H2 through the
        Sites; (c) advertising and sponsorship frequency discounts actually
        payable; and (d) *."

        2. Section 1.16 (Definition of Site) is hereby amended and restated in
its entirety to read as follows:

                "1.16 "Site" means one or more Web sites established and
        maintained by N2H2 through which end users may access the Inktomi Search
        Engine and run searches against the Database. "Site" also includes all
        sites linked to N2H2's Web sites so as to access the Inktomi Search
        Engine as authorized under Section 2.1.1."

        3. A new Section 2.1.1 is hereby added to the Agreement as follows:


<PAGE>   2
(*) INFORMATION HAS BEEN OMITTED PURSUANT TO A REQUEST FOR CONFIDENTIAL
TREATMENT AND HAS BEEN FILED SEPARATELY WITH THE SECURITIES AND EXCHANGE
COMMISSION.

                                                                   EXHIBIT 10.16

                "2.1.1 Distribution Rights. N2H2 may make results sets generated
        through search queries against the Database available to end-users of
        third party Web sites subject to the provisions of this Section and all
        other terms and conditions of this Agreement. N2H2 may make the results
        sets available only in connection with the distribution of N2H2's search
        services to such third party sites and for no other purpose. No Inktomi
        Technology may be provided to such sites, and, unless otherwise agreed
        in writing by Inktomi, the results sets shall be made available only
        through N2H2 servers or similar means which prevent direct access to the
        Inktomi Search Engine by such third party end users. N2H2 will provide
        such services only pursuant to a written agreement which is at least as
        protective of the Inktomi Technology as the terms of this Agreement and
        which contains a disclaimer of all warranties and limitations of
        liability on behalf of Inktomi in a form reasonably acceptable to
        Inktomi. N2H2 will provide Inktomi a monthly report that sets forth the
        third parties that have entered into a distribution relationship as
        contemplated above."

        4. Section 3.3 (House Ads) is hereby deleted from the Agreement.

        5. Section 6.1 (Service Fees) is hereby amended and restated in its
entirety to read as follows:

                "6.1 Service Fees. N2H2 shall pay the fees set forth in this
        Section 6.1 and Exhibit A. N2H2 shall pay Inktomi monthly service fees
        equal to the sum of (a) the Per-Hit Charge (as defined below) for such
        month attributable to Hits generated by distribution partners of N2H2 as
        described in Section 2.1.1; plus (b) the greater of (i) the Per-Hit
        Charge (as defined below) for such month attributable to Hits generated
        directly by N2H2 from Sites or (ii) * of Net Revenues for such month.
        Notwithstanding the foregoing, N2H2 shall pay Inktomi a minimum of * for
        the first year under this Agreement and * for each subsequent year under
        this Agreement (with one-third attributable to Filtering Services and
        two-thirds attributable to the Search Services). For the first year, the
        minimum shall be paid as follows: * shall be paid upon execution of this
        Agreement (which Inktomi acknowledges has been paid); * shall be paid on
        or before January 31, 1998 (which Inktomi acknowledges has been paid); *
        (or the monthly service fees as computed in the first sentence above if
        such fees are greater than *) shall be paid on each of October 31, 1998,
        November 30, 1998 and December 31, 1998; and the balance of the first
        year minimum shall be paid on the earlier of October 31, 1998 or the
        closing date of a capital-raising transaction by N2H2. Inktomi
        acknowledges and agrees that N2H2 has paid the amounts required owed in
        1998. For subsequent years (beginning January 1999), the minimum shall
        be paid in equal monthly installments of *. Two-thirds of all such
        minimum payments shall be credited against monthly service fees paid or
        payable for such year. Monthly service fees shall be paid in arrears
        within thirty (30) calendar days following the end of each month.

                The "Per-Hit" Charge for each month shall be based on the total
        number of Hits served during the month. These fees equal:

                (A)     the total number of Hits served during the month divided
                        by the total number of days in such month ("Average
                        Daily Hits Served"),

                (B)     multiplied and added in accordance with the following *:


                         *                         *

                         *                         *


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<PAGE>   3
(*) INFORMATION HAS BEEN OMITTED PURSUANT TO A REQUEST FOR CONFIDENTIAL
TREATMENT AND HAS BEEN FILED SEPARATELY WITH THE SECURITIES AND EXCHANGE
COMMISSION.

                                                                   EXHIBIT 10.16

                         *                         *

                         *                         *

                         *                         *

                         *                         *

                (C)     multiplied by the total number of days in such month."

        6. Exhibit A (Services) is hereby amended to provide the following:

                a.      Inktomi will use its commercially reasonable efforts to
                        tag the Database with an updated N2H2 Filter List on a
                        daily basis; provided, that N2H2 provides Inktomi an
                        updated N2H2 Filter List each day.

                b.      The parties acknowledge and agree that the number of
                        tags included in the N2H2 Filter List shall be increased
                        from * to *. Such tags are set forth on Schedule 1.

                c.      N2H2 shall pay Inktomi a non-recurring engineering fee
                        of * in consideration of the initial tagging of the
                        Database with the N2H2 Filter List. Such payment shall
                        be made by N2H2 within thirty (30) days of the Effective
                        Date.

        7. For the provision of the services set forth in Exhibit A as amended
above, in addition to the fees currently to be paid by N2H2 under the Agreement,
Inktomi will charge N2H2 the following fees:

                a.      An annual Information Service fee of * to be paid in
                        twelve (12) monthly installments of * to be paid as part
                        of N2H2's monthly service fees, provided that when N2H2
                        exceeds an average daily hit rate of 500,000 queries per
                        day, such monthly Information Service fee shall decrease
                        as follows:


<TABLE>
<CAPTION>
                   Queries Per Day         Monthly Information Service Fee
                   ---------------         -------------------------------
<S>                                        <C>
                       500,000                            *
                       600,000                            *
                       700,000                            *
                       800,000                            *
                       900,000                            *
                     1,000,000 +                          *
</TABLE>


        8. Section 10.1 ("Term") is hereby amended to continue in force for a
period of three years following the effective date of this amendment, unless
earlier terminated as provided in the agreement.

        9. All capitalized terms not otherwise defined herein shall have the
meanings given them in the Agreement, unless the context otherwise requires.

        10. Except as amended by this Amendment, the Agreement shall remain in
full force and effect.


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<PAGE>   4
                                                                   EXHIBIT 10.16

        IN WITNESS WHEREOF, the parties have caused this Amendment to be signed
by their duly authorized representatives.

N2H2, INC.                         INKTOMI CORPORATION

By:     /s/ John Duncan            By:      /s/ Dennis L. McEvay
   -------------------------          -------------------------------
Title:  CFO                        Title:   Vice President
      ----------------------             ----------------------------
Date:   6-30-99                    Date:    6/30/99
     -----------------------            -----------------------------


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