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EXHIBIT 31.1 CERTIFICATION OF CHIEF EXECUTIVE OFFICER
AS ADOPTED PURSUANT TO
SECTION 302 OF THE SARBANES-OXLEY ACT OF 2002 I, Steven G. Mihaylo, certify that:  1.
    I have reviewed this annual report on Form 10-K of Inter-Tel, Incorporated;2.
    Based on my knowledge, this annual report does not contain any untrue statement of
a material fact or omit to state a material fact necessary to make the statements made,
in light of the circumstances under which such statements were made, not misleading with
respect to the period covered by this annual report;3.
    Based on my knowledge, the financial statements, and other financial information
included in this annual report, fairly present in all material respects the financial
condition, results of operations and cash flows of the registrant as of, and for, the
periods presented in this annual report;4.
    The registrants other certifying officers and I are responsible for establishing
and maintaining disclosure controls and procedures (as defined in Exchange Act Rules
13a-15(e) and 15d-15(e)) and internal control over financial reporting (as defined in
Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant and we have:  a)
    designed such disclosure controls and procedures, or caused such disclosure
controls and procedures to be designed under our supervision, to ensure that material
information relating to the registrant, including its consolidated subsidiaries, is
made known to us by others within those entities, particularly during the period in
which this annual report is being prepared;b)
    designed such internal control over financial reporting, or caused such
internal control over financial reporting to be designed under our supervision, to
provide reasonable assurance regarding the reliability of financial reporting and the
preparation of financial statements for external purposes in accordance with
generally accepted accounting principles;c)
    evaluated the effectiveness of the registrants disclosure controls and
procedures and presented in this annual report our conclusions about the
effectiveness of the disclosure controls and procedures, as of the end of the period
covered by this annual report based on such evaluation; andd)
    disclosed in this annual report any change in the registrants internal
control over financial reporting that occurred during the registrants most recent
fiscal quarter (the registrants fourth fiscal quarter in the case of an annual
report) that has materially affected, or is reasonably likely to materially affect,
the registrants internal control over financial reporting; and  5.
    The registrants other certifying officers and I have disclosed, based on our most
recent evaluation of internal control over financial reporting, to the registrants
auditors and the audit committee of registrants board of directors (or persons
performing the equivalent functions):  a)
    all significant deficiencies and material weaknesses in the design or
operation of internal control over financial reporting which are reasonably likely to
adversely affect the registrants ability to record, process, summarize and report
financial data; andb)
    any fraud, whether or not material, that involves management or other
employees who have a significant role in the registrants internal control over
financial reporting. /s/ STEVEN G. MIHAYLODate: March 14, 2005
    
    Steven G. MihayloChairman and Chief Executive Officer (PrincipalExecutive Officer)