We make a case for setting initial conditions for inflation at the Planck epoch in the kinetically dominated regime. For inflationary potentials with a plateau or a hill, i.e., potentials that are bounded from above within a certain region of interest, we cannot claim complete ignorance of the energy distribution between kinetic and potential energy, and equipartition of energy at the Planck epoch becomes questionable. We analyze different classes of potentials in phase space and quantify the fraction of the Planck surface that is kinetically dominated. Considering bounded potentials with very small amplitudes as favored by current data and restricting ourselves to the domains of phase space that are of interest to cosmic inflation, we find that initial conditions of the inflaton field should be set in the kinetically dominated regime regardless of any choice of prior.