How to solve recursion with two seperate converges rates

What is the correct way to solve the following recursion: $ T(n)=T(\lceil\frac{n}{2}\rceil) + T(n-2)$

Or basically any recursion that has two parts which converge in a different rate.

I’m trying to get big $ O$ approximation, as tight as possible, but I couldn’t figure it out with any "traditional" approach.