Downward collapse (also known as upward separation) refers to cases wh
ere the equality of two larger classes implies the equality of two sma
ller classes. We provide an unqualified downward collapse result compl
etely within the polynomial hierarchy. In particular, we prove that, f
or k >2, if P-Sigma kp[1] = P Sigma(kp[2]) then Sigma(k)(p) = Pi(k)(p)
= PH. We extend this to obtain a more general downward collapse resul
t.