We consider the initial value problem with boundary control for a scalar nonlinear conservation law(*) u(t) + [f(u)](x) = 0, u(0,x) = 0, u(.,0) = (u) over tilde is an element of U,on the domain Omega = {(t,x) is an element of R-2 : t greater than or equal to 0, x greater than or equal to 0}. Here u = u(t,x) is the state variable, U is a set of bounded boundary data regarded as controls, and f is assumed to be strictly convex. We give a characterization of the set of attainable profiles at a fixed time T > 0 and at a fixed point (x) over bar > 0:Moreover we prove that A(T,U) and A ((x) over bar,U) are compact subsets of L-1 and L-loc(1), respectively, whenever U is a set of controls which pointwise U satisfy closed convex constraints, together with some additional integral inequalities.