We give stopped Doob inequalities for p-th moment, 0<p<∞, of stochastic convolution integrals ∫_(0,t]U(t,s)φ_s^- dM_s in a Hilbert space, where M is a Hilbert space-valued cadlag square integrable martingale, φ is an operator-valued predictable process and U(t,s) is a contraction-type evolution operator. We also generalize the previous results and try to get smaller constants.