Algorithms based on the QR decomposition of the equivalent space-time channel matrix have been proved useful in the detection of V-BLAST systems. Especially, the parallel detection (PD) algorithm offers ML approaching performance up to 4 transmit antennas with reasonable complexity. We show that when directly applied to STBCs, the PD algorithm may suffer a rather significant SNR degradation over ML detection, especially at high SNRs. However, simply extending the PD algorithm to allow p ${geq}$ 2 candidate layers, i.e. p-PD, regains almost all the loss but only at a significant increase in complexity. Here, we propose a simplification to the p-PD algorithm specific to STBCs without a corresponding sacrifice in performance. The proposed algorithm results in significant complexity reductions for moderate to high order modulations.