In modern wireless communication devices, cost- and area-effective signal processing architectures are essential. Flexible and reconfigurable front-end solutions are necessary to achieve high-spectral efficiency. Direct conversion transceivers are suitable but have to deal with I/Q mismatch, for which large bandwidths become frequency selective. Blind I/Q mismatch compensation can be based on a statistical property called properness, which is fulfilled for a large class of digitally modulated communication signals and which is destroyed by I/Q mismatch. We propose a novel DSP-algorithm for blind adaptive I/Q mismatch compensators using only real-valued filters, which rebuilds this properness in two stages. Additionally, we add a simple compensation solution for dc offset which can be integrated in the I/Q mismatch compensator. In a detailed analysis, we prove that nonlinear even-order distortions resulting from finite mixer isolation have only negligible influence on properness under realistic impairment levels. A stability analysis exhibit conditions of those compensator parameter regions for which the optimal steady-state is asymptotically stable. For practical frequency-independent I/Q mismatch values, we show that the algorithm converges with a suitable initial value to the optimum steady state. The proposed algorithm outperforms other state-of-the-art algorithms while its computational complexity is reduced. Results from a 3GPP LTE downlink simulator support the analysis.