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We show that for a simple graph $G$, $c'(G)\leq\Delta(G)+2$ where $c'(G)$ isthe choice index (or edge-list chromatic number) of $G$, and $\Delta(G)$ is themaximum degree of $G$.  As a simple corollary of this result, we show that the total chromatic number$\chi_T(G)$ of a simple graph satisfies the inequality $\chi_T(G)\leq\\Delta(G)+4$ and the total choice number $c_T(G)$ also satisfies thisinequality.  We also relate these bounds to the Hall index and the Hall condition index ofa simple graph, and to the total Hall number and the total Hall conditionnumber of a simple graph.

Bounds Related to The Edge-List Chromatic and Total Chromatic Numbers of a Simple Graph