Traditional two-photon excitation suffers from two difficulties that prevent complete population transfer: dynamic Stark shifts and multiphoton ionization. We describe a technique for overcoming these limitations by using a second field to control dynamic Stark shifts via Stark-chirped rapid adiabatic passage (SCRAP) and simultaneously suppress undesired photoionization via laser-induced continuum structure (LICS). We illustrate this proposed procedure by numerical simulations of two-photon excitation of the metastable state of hydrogen, showing that efficient excitation can be expected when the two laser pulses are properly crafted.