  We compute the proton structure function F_2^p at small x and large Q^2 at
next-to-leading order in alpha_s(Q^2), including summations of all leading and
subleading logarithms of Q^2 and 1/x in a way consistent with momentum
conservation. We perform a detailed comparison to the 1993 HERA data, and show
that they may be used to determine alpha_s(M_Z^2)=0.120 pm 0.005(exp) pm
0.009(th). The theoretical error is dominated by the renormalization and
factorization scheme ambiguities.
