Mattress protectors

Hello everyone,

I am looking at getting a mattress protector for my carrycot (which I will use as baby's first bed in place of a Moses basket. I have been looking at dri cot woollen mattress protectors and the woollen ones from Nature Baby. Obviously I will need one for the cot too when he goes in there. My question is, is it safe to have a mattress protector that's a bit big in the carrycot, I can't seem to find one small enough for the carry cot. Anyone had any experience with mattress protectors for carrycots?

Thanks