I found a totally fab sleeveless top at Macys. It's called a "tank" but I would call it a sleeveless blouse.

Woven polyester but NOT sticky or uncomfortable, probably in part because it's a fluid/breeze style. Banded neck, pleat in front, gathered shoulders and back yoke, which all make it a little more interesting than a plain vneck tank. Could be tucked in I suppose but I did not. Machine washable.

The petite fit is absolutely perfect on 5'1" short waisted me which is an extreme rarity in sleeveless tops. ( I usually find too-low armholes, too-long body length, armhole gaping, and/or or a too-low neckline.) Good length too, hits me right around/above the crotch point.

No photos, but wore the lemon yellow one last weekend to a backyard barbeque where it was in the high 80's F and very humid. Super comfortable. Did not cling at all. Wrinkles just a little but shakes out. Dressier than a tee/tank but still relaxed and casual.

I bought 3 in white, lemon yellow, and golden yellow. For petites, it also comes in a soft blue and a color called cranberry spice. Showing all the petite colors.

Also comes in regular sizes in over a dozen colors including the green shown.