By actual survey, the 13th step on the west front of the State Capitol building at this city's center is 5,280.0 feet above sea level, an altitudinal nicety that has provided Denver an identity for decades.

By far the most popular commercial and promotional adjective here in the Mile-High City is, naturally, "Mile-High" -- as in Mile-High Stadium, Mile-Hi Cablevision, and enough other Mile-High (or -Hi) shops, parks, schools and churches to fill four columns of the Denver telephone directory.

But now the city has launched a campaign to find a new capsule description, condemning "Mile-High" to the burial ground for outmoded images. There it will join a 19th-Century Denver motto -- "Queen City of the Plains" -- that disappeared when local leaders decided that the nearby mountains had more allure to easterners than the nearby plains.

The rap on "Mile-High" among the high and mighty here is that it evokes an image of a snowbound alpine outpost populated exclusively by skiing fans and four-wheel-drive enthusiasts.

Denver's energetic and intensely image-conscious mayor, Federico Pena, complains that this picture is grossly exaggerated -- the city is dry and sunny most of the year -- and that it misses the point of Denver's emergence as a youthful, prosperous regional Capital.

Pena and civic leaders such as Richard Fleming, head of a downtown group called The Denver Partnership, have mounted a campaign to attract new businesses and up-scale retailers like Saks Fifth Avenue and Bloomingdales. To do that, Fleming says, it is important to convey the message that Denver is "Yuppieland to the Nth degree."

When a new shopping mall housing a branch of Brooks Brothers, the ultimate Yuppie haberdashery, opened here last fall, the occasion was treated as a civic coup. Leaders of business and government turned out in droves the day the mall opened for business. The main speaker was the mayor, who began his address with these words: "It's not snowing."

In this climate, it is not surprising that Pena was affronted when, at Chicago's O'Hare International Airport, he saw a Denver travel poster that depicted a snowcapped-mountain scene.

As soon as his plane landed in Denver, the mayor called in a dozen public relations specialists and challenged them to come up with something better than "Mile-High."

The result has been a riot of confusing and often conflicting municipal image-making that has swept the city this spring.

Last month, the public relations experts unveiled an ornate banner emblazoned with the motto: "Denver -- What a Place to Be!" This offering was immediately denounced as drab and unoriginal. (Los Angeles, after all, has been promoting "L.A.'s the Place!" for years.)

Tom Gavin, the witty Denver Post columnist, wrote that almost anybody could do better than that, and proposed a few alternatives: "Denver -- A City in Colorado;" "Denver -- Birthplace of Vaunda Hinkle;" "Denver -- Warmer Than Minnesota, More Fun Than Nebraska!"

Then Fleming's downtown boosters got into the act, observing that the real image problem here is not the snow but, rather, the notion that Denver is a "cow town."

When he tries to sell Denver to eastern business types, Fleming complained, "The first thing they ask you about is, 'Are the steers still loose on the streets?' "

Fleming's group, accordingly, laid out plans for a four-part promotional campaign, complete with a "Denver Today" newsletter and an office in media-rich Manhattan to sell Denver as an urban mecca where affluent young professionals far outnumber cows.

The Chamber of Commerce joined the fray last week with its own new image campaign flaunting both the "Mile-High" and the "cow-town" dimensions of the city.

The chamber's first advertisement features author Leon Uris -- a resident of Aspen, a mountain town 162 miles west of here -- promoting Denver as "an ideal environment for the creative person."

The new ad depicts a Denver skyline as the backdrop for a drawing of Uris wearing a big cowboy hat. Above the hat is another new city slogan: "Denver. By a Mile."

As a final element in the image overhaul, the city's American Association baseball team this season has dropped its rustic, mountain-like traditional name -- "Denver Bears" -- and adopted the less conventional label "Denver Zephyrs."

This change is a boon to sports-page headline writers: "Zesty Z's Zap Cubs 7-0." But local literati point out that "Zephyr" was the ancient Greeks' name for the west wind -- the very wind that brings on the mighty mountain snows most people still associate with the Mile-High City.