It is well-known that the fundamental group of a twice-punctured torus is a free group of rank three. 

I see that there is no one-to-one correspondence between the homotopy classes of essential simple loops on twice-punctured torus and the conjugacy classes of primitive elements in a free group of rank three. 

Do we know which primitive elements in a free group of rank three represent simple loops on a twice-punctured torus?