A new regime of laser wakefield acceleration of an injected electron bunch is described. In this regime, the bunch charge is so high that the bunch wakefields play an important role in the bunch dynamics. In particular, the transverse bunch wakefield induces a strong self-focusing that suppresses the transverse emittance growth arising from misalignment errors. The decelerating longitudinal bunch wakefield, however, is not so strong that it completely cancels the accelerating laser wakefield. In fact, the induced energy spread can be compensated by exploiting phase slippage effects. These features make the new regime interesting for high beam quality laser wakefield acceleration.