This paper introduces a new constrained adaptive subband beamformer algorithm for speech enhancement in acoustic telecommunication systems. The solution relies on a pre-calculated source covariance matrix and recursive estimates of background noise- and handsfree signal covariance matrices. The constraint acts as an eye-opening in a vicinity of the near-field location of the source and degradations from steering-vector errors can therefor be made small. The algorithm is applied in subbands using a uniform multi channel over-sampled filterbank. Simulations with real speech recorded in an automobile hands-free environment show 19 dB noise reduction and 20 dB hands-free suppression.