We present results for heavy-light decay constants, using both propagating quarks and the static approximation, in O(a)-improved, quenched lattice QCD. At beta=6.2 on a 24^3x48 lattice we find f_D=185 +4-3(stat)+42-7(syst) MeV, f_B=160 +6-6 +53-19 MeV, f_{D_s}/f_D=1.18 +2-2 and f_{B_s}/f_B=1.22 +4-3, in good agreement with earlier studies. From the static theory we obtain f_B^stat=253 +16-15 +105-14 MeV. We also present results from a simulation at beta=6.0 on a 16^3x48 lattice, which are consistent with those at beta=6.2. In order to study the effects of improvement, we present a direct comparison of the results using both the Wilson and the improved action at beta=6.0.