This talk describes experiments exposing Rydberg atoms to short, intense pulses of a linearly polarized microwave field consisting of two phase-locked frequencies whose relative phase $\phi$ can be varied. The same apparatus was used for experiments on two different atoms. In experimental-theoretical work carried out with S. Zelazny and L. Sirko, helium atoms prepared in the (1sns)^3S_1 Rydberg state with n near 30 were used to investigate how important $\phi$ is as a strong-field, quantum-control parameter when the frequency ratio p:q is varied. The p:q dependence has not been specifically addressed before experimentally, but it will become important when high-harmonic-generation sources driven by ultrashort-pulse lasers are developed as workaday laboratory tools. In experimental-theoretical work carried out with L. Sirko, hydrogen atoms prepared with, e.g., principal quantum number n=51 were used to make the first study of the role of common resonances in ionization by microwave fields. These pendulumlike resonances require the presence of both driving frequencies and allow use of $\phi$ as a control parameter. Classical and quantal calculations, which agree nicely, are used to understand the phase sensitivity. There are some similarities between these common resonances and nonlinear resonances in our solar system involving three bodies orbiting a fourth.