  Let p be an odd prime number. We describe the Whitehead group of all
extra-special and almost extra-special p-groups. For this we compute, for any
finite p-group P , the subgroup Cl\_1 (ZP) of SK\_1 (ZP), in terms of a genetic
basis of P. We also introduce a deflation map Cl\_1 (ZP) $\rightarrow$ Cl\_1
(Z(P/N)) , for a normal subgroup N of P , and show that it is always
surjective. Along the way, we give a new proof of the result describing the
structure of SK\_1 (ZP), when P is an elementary abelian p-group.
