This note provides several remarks relating to the conditional choice probability (CCP) based estimation approaches for dynamic discrete-choice models. Specifically, the Arcidiacono and Miller (2011) estimation procedure relies on the ”inverse-CCP” mapping ψ(p) from CCPs to choice-specific value functions. Exploiting the convex-analytic structure of discrete choice models, we discuss two approaches for computing this mapping, using either linear or convex programming, for models where the utility shocks can follow arbitrary parametric distributions. Furthermore, the ψ function is generally distinct from the ”selection adjustment” term (i.e. the expectation of the utility shock for the chosen alternative), so that computational approaches for computing the latter may not be appropriate for computing ψ.