What's the secret to finding a bra that doesn't show through dress and top sleeves?

[Thesunrising]

So annoying. I have to wear fairly sturdy bras, 36d and e but not totally massive, but there's hardly a top or dress I have that you can't see a good chunk of the bra through the armhole (short sleeves, cap sleeves and sleeveless stuff)

Are there special bras that are lower cut under the arm pit so it's not so visible? It really makes an outfit look untidy to have my smalls on display :-(

I had to wear my M&S sports bra today as it was the only bra I had that didn't show it's straps under the dress I wanted to wear.