  We describe an effective version of the conjugacy problem and study it for
wreath products and free solvable groups. The problem involves estimating the
length of short conjugators between two elements of the group, a notion which
leads to the definition of the conjugacy length function. We show that for free
solvable groups the conjugacy length function is at most cubic. For wreath
products the behaviour depends on the conjugacy length function of the two
groups involved, as well as subgroup distortion within the quotient group.
