We show that binary circular words of length n avoiding 7/3+ powers exist for every sufficiently large n. This is not the case for binary circular words avoiding k+ powers with k < 7/3

We show that there exist binary circular 5/2+ power free words of every length.

We show that the number of ternary words of length n avoiding abelian cubes grows faster than r^n, where r = 2^{1/24}