  Determining the length of short conjugators in a group can be considered as
an effective version of the conjugacy problem. The conjugacy length function
provides a measure for these lengths. We study the behaviour of conjugacy
length functions under group extensions, introducing the twisted and restricted
conjugacy length functions. We apply these results to show that certain
abelian-by-cyclic groups have linear conjugacy length function and certain
semidirect products $\Z^d \rtimes \Z^k$ have at most exponential (if $k >1$) or
linear (if $k=1$) conjugacy length functions.
