Aligning without overaligning memory

I would like to allocate some byte buffers, to be passed to an external function, that have specific minimally aligned requirements.

The requirement is that the buffer be aligned to a N-byte¹ boundary, but not to a 2N boundary. For example, if N is 64, then an address p should satisfy p % 64 == 0 and p % 128 != 0.

Is there a reasonable way to do this with the standard facilities of C++11?

If not, is there is a reasonable way to do this outside the standard facilities² which works in practice for modern compilers and platforms?

The buffer will be passed to an outside routine (adhering to the C ABI but written in asm). The required alignment will usually be greater than 16, but less than 8192.

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¹ As usual, N is a power of two.

² Yes, I understand an answer of this type causes language-lawyers to become apoplectic, so if that's you just ignore this part.