<PAGE>   1
                                                                    EXHIBIT 99.1



                 SPECIALTY TELECONSTRUCTORS RENAMED OMNIAMERICA

                            -NEW TICKER SYMBOL:XMIT-

        -NEW NAME BETTER REFLECTS COMPANY'S WIDE RANGE OF CAPABILITIES-

ALBUQUERQUE, New Mexico, September 15, 1998 - Specialty Teleconstructors, Inc.
(Nasdaq: SCTR) today announced that it has changed its name to OmniAmerica,
Inc. and that it now trades on the Nasdaq Stock Market under a new ticker
symbol, XMIT.  The Company was formed in April through the merger of Specialty
Teleconstructors, Inc. and OmniAmerica Holdings.  At the time of the merger, it
was announced that the combined company would initially be known as Specialty
Teleconstructors and that it would trade under that company's ticker symbol,
but soon be renamed OmniAmerica.

The merger of OmniAmerica and Specialty Teleconstructors created a leading
full-service national transmission tower company, and the OmniAmerica name
better reflects the company's wide range of tower-related capabilities.
OmniAmerica's stated strategy is to accumulate owned and managed sites for its
own account through acquisition and utilization of its site acquisition and
construction resources, in addition to providing outside construction and site
implementation services to the wireless communications and broadcasting
industries.

A majority of the Company's shareholders have approved the name change, as well
as the Company's reincorporation in Delaware.

The matters discussed in this press release contain forward-looking statements
within the meaning of Section 21E of the Securities Exchange Act of 1934, as
amended.  Forward-looking statements involve risks and uncertainties which
could cause actual results to differ materially from the forward-looking
information.  Such risks and uncertainties include, but are not limited to, the
following possibilities: increasing competition for tower sites, increasing
difficulty in obtaining zoning and construction permits, difficulties in
integrating acquisitions, changes in regulatory requirements, changes in
telecommunications transmission technology, changes in outsourcing plans of
telecommunications transmission companies and factors inherent in tower
ownership and construction, such as the availability of experienced
construction crews and damage and delays caused by inclement weather.  A
description of these factors, as well as other factors which could affect the
company's business, is set forth in filings by the company with the Securities
and Exchange Commission.

                                     -more-
<PAGE>   2
                                                                               2


OmniAmerica, Inc. owns, manages and develops multi-use telecommunications sites
for radio and television broadcasting, paging, cellular, PCS and other wireless
technologies; provides wireless infrastructure building and implementation
services primarily for providers of wireless communication services in the
United States; and manufactures and sells wireless infrastructure components
used in the construction and maintenance of wireless communication transmitting
and receiving facilities.  The Company has 26 field offices nationwide with
corporate executive offices in Cedar Crest (Albuquerque), New Mexico,
Cleveland, Los Angeles and West Palm Beach, Florida.  OmniAmerica owns, has
agreed to acquire or is currently constructing/developing for its own account a
total of approximately 800 towers.

                                     # # #