Due to their simplicity, low power consumption, and high-performance, direct conversion transceivers are used widely in RF-front ends. Direct conversion receivers demodulate the signal to its in-phase (I) and quadrature (Q) parts by multiplying the RF signal with two signals with a 90° phase separation. To achieve best performance, I and Q paths should be matched in terms of gain, phase, and have no DC offset. Any impairment in these parameters would result in reduced performance and higher bit error rate. In this work, we propose a BIST scheme for IQ mismatch compensation with low overhead for direct conversion receivers. We use an envelope detector to detect the combined amplitude of the I and Q signals and we use this information to iteratively correct for the receiver's IQ imbalance. The only requirement on the power detector is a small linear dynamic range (15dB). The conversion gain of the power detector does not need to be known. The proposed method can be used in the mission mode in the background to calibrate any deviations in performance. After the receiver's IQ imbalance is corrected, it can be used to measure and compensate for any transmitter IQ imbalance in a loopback mode. Simulations and hardware measurements confirm that the proposed technique can measure the imbalances with high accuracy.