I want to record some of my rides, and also any incidents that may happen when I'm out riding.

I'm looking for a neat, discreet and good quality helmet camera that doesn't look awkward and odd (e.g. the GoPro cams that are just too big and the wrong shape for helmet cameras).

Any recommendations? I don't need spectacularly specced action cameras as all I want to do is record simple, high quality video in 1080p as a minimum.

Budget would be up to 300 USD.