In dual-band transmitarrays, unit-cell design becomes more challenging, since simultaneous and related strict phase specifications at both bands must be met (e.g., to enable beam-steering trough mechanical displacement of the feed). In this work, we present an efficient methodology for unit-cell design based on an ad-hoc implementation of the spectral-domain method of moments (SD-MoM), which computes the full-wave unit-cell response at an affordable computational expense (two to four orders of magnitude lower than general-purpose commercial software). An innovative approach consisting of a genetic-algorithm assisted search of unit-cell solutions is carried out. This approach can be applied because of the efficiency and full-wave accuracy provided by SD-MoM in each fitness function evaluation. As an application example, a set of unit cells is designed to operate in the satellite communications Ka-bands 19.7-20.2 GHz and 29.5-30 GHz. The achieved unit cells have a much lower profile than previous designs for the same bands.