We have demonstrated that appropriately time-ordered pulses of diode-laser light can provide efficient population transfer in a three-level cascade system. Laser-trapped Rb atoms are excited from the 5S ground state to the highly-excited 5D level (via the 5P interdediate level) with a transfer efficienty approaching 100%. Diode laser light at 780 nm (5S->5P) and 776 nm (5P->5D) is switched with acousto-optic modulators to provide the excitation. The measured variation of transfer efficiency with relative delay between the two pulses is in reasonable agreement with theoretical predictions. However, the intensities needed for efficient transfer are significantly higher than expected. In general, optimum excitation occurs for the counterintuitive pulse ordering, i.e., when the upper transition is driven first.