Numerically calculated space-charge-limited current-voltage curves are presented for an insulator with one ohmic electrode (infinite injected charge density) and one blocking electrode (finite injected charge density). Charge-carrier diffusion is included, and traps in the insulator are assumed to be absent, shallow, or exponentially distributed in energy. The transition from bulk to surface limitation of the current (when the charge density is large but finite at the injecting electrode) is discussed with reference to the validity of the diffusion-free theory. A modification of the constant-field approxi- mation is shown to give a good description of the current-voltage curve when the injected charge density at the blocking electrode is small, and the current lies well below the purely space-charge-limited current which would flow if both electrodes were ohmic.