In an orthogonal frequency division multiplexing (OFDM) receiver with direct-conversion architecture, carrier frequency offset (CFO) and direct-current offset (DCO), which cause severe performance degradation, need to be estimated and compensated. Recently, by investigating the subspace of OFDM signal after coarse DCO cancellation using timedomain average, we have proposed a nullspace-based estimator (NSE), for blind CFO and DCO estimation. In this paper, based on an analysis of the cost function of the NSE, we propose a common nullspace based estimator (CNSE). It is shown that by matching the frequency occupation of the received OFDM signal with CFO and DCO, the CNSE can achieve the full performance potential of the NSE. Also, the performance analysis reveals that the CNSE can asymptotically approach the Cramer-Rao bound (CRB) of OFDM CFO estimation in the presence of DCO. Finally the analysis results are confirmed by simulations.