Wide angle beam steering is a fundamental requisite for the new generation of millimeter waves communication systems. Mechanical scanning using two transmit-arrays (TAs) with independent axial rotation movements - known as the Risley prism approach - is being considered as a potential enabling technology for many cost-driven applications. There is an ongoing research effort to improve this solution, however, grating lobes are still a main limitation for the operation of these antennas. Herein, we show that this vestigial effect can be overcome by a co-design of the phase correction of the two rotating surfaces, instead of considering each TA as a separate “prism” (the conventional approach). The proposed generalized phase correction is compared with the conventional counterpart using a design example based on fully dielectric TAs. Experimental results confirm that the predicted grating lobes of the conventional design can be mitigated, corresponding to a significant reduction of the side lobe level (SLL) in the complete scanning plane. For the given full-dielectric Ka-band design example, is possible to scan up to 55 degrees with SLL<-8.3 dB and scan loss of -3.6 dB, whereas, with the conventional approach, the same scan implies SLL< -4.4 dB and a scan loss of -6.1 dB