We introduce a method for estimating crustal thickness and bulk crustal and upper‐mantle shear‐wave velocities directly from high‐quality measurements of fundamental‐mode Rayleigh‐wave dispersion in the period range from 10 to 40 s. The method is based on an approximate Rayleigh‐wave dispersion formula and provides fast results with minimal model parameterization. We apply the method to Rayleigh‐wave phase maps in Alaska to reveal first‐order structure in a region that had not been systematically and densely instrumented prior to the Transportable Array (TA). To demonstrate the consistency of the results, we also apply the same method to existing Rayleigh‐wave phase maps derived from TA data in the conterminous United States, where crustal and upper mantle structures are better known. We contrast features observed in maps of crustal thickness and bulk shear‐wave velocity between the Cascadia and Alaska‐Aleutian subduction zones to highlight differences in the two regions. Our results show that, contrary to conventional wisdom, first‐order information on the location of major depth discontinuities (e.g., the Moho) can be extracted in a fast, straightforward manner from measurements of Rayleigh‐wave dispersion alone.