Many of us who are more endowed in size, shape and/or breast weight do have certain bras we wear with certain clothes or looks to help minimize the effect. I too am D+ in size and I have lace bras, tee-shirt bras, underwire, soft cup, sleep bra, seamed bras, all for support/comfort and containment. I too am modest when it comes to advertising my support garments. The right bra for the right clothing and event goes a long way of staying under the radar. It's something women are experts at and we can learn too.
Bras are not styled and embellished with men in mind so if you want something that supports, contains and is comfortable, the support garment will not look very manly sometimes. It's the price you pay for the comfort, support and containment you seek and enjoy when endowed beyond the norm.