The influence of nonideal effects associated with ionization upon the dynamics and thermodynamics of compressible convection is studied. Linear and finite-amplitude analyses and fully nonlinear two-dimensional simulations of a plane-parallel layer of single-atomic-level hydrogen fluid are undertaken. Ionization significantly influences both the global transport properties and the local dynamics of convective flows by modifying the particle number density, specific heat, and internal energy content of the fluid. Strong temperature fluctuations and corresponding buoyancy forces develop locally in the fluid wherever rapid changes in ionization state occur. These can result in narrow regions of intense vertical flow. The flow asymmetries seen in simulations of compressible ideal-gas convection can either be enhanced or diminished depending on the vertical positioning of the partially ionized region within the domain. Additionally, the enthalpy flux achieved by ionizing convection is dominated in regions of partial ionization by latent-heat transport. The enthalpy carried by downflow plumes can be considerably elevated, and the cancellation between kinetic energy and enthalpy fluxes observed in the downflows in some simulations of ideal gas turbulence may thus be offset by partial ionization of the fluid. Such ionization effects are likely to influence the character of convective motions within stellar envelopes. Convective transport properties may differ substantially between the partially ionized and the deeper fully ionized regions of a star, and since ionization zone placement also varies with respect to both the photosphere and the lower thermal boundary, between stellar types and during the course of stellar evolution.