A typical approach to reduce speckle in coherent imaging systems, is to average same-target images with different speckle realizations. We study settings where such realizations come from applying different transducer-array element-weights at reception, referred to here as receive compounding. An effect of such compounding is reduced spatial resolution, causing smearing of point-like image structures, filling of cysts and expansion of hyperechoic regions. In this paper we study how these unwanted effects can be mitigated by combining the compounding with a small, phase-based, adaptive steering of the array at reception. The adaptivity is based on a criterion akin to that of the Capon beamformer; a minimum-output distortionless response. Here, the distortionless part ensures that however we steer, we have a uniform at-focus response. We have applied this adaptive steering in combination with several receive compounding techniques on simulated Field II, phantom and in vivo data. The results show that all the studied compounding techniques respond to this positively in light of the mentioned unwanted effects. The technique based on Thomson’s multitaper method even surpassed the non-compounded equivalent in reproducing the geometry of structures. The speckle reduction, as measured by the change in the pixel mean to standard deviation ratio, is indeed lower, and there are subtle changes in the spatial speckle patterns when applying steering; however, we believe that in most cases the negative effects are tolerable in light of the benefits gained. The suggested approach is intuitive and easily implemented.