  The cop throttling number $th_c(G)$ of a graph $G$ for the game of Cops and
Robbers is the minimum of $k + capt_k(G)$, where $k$ is the number of cops and
$capt_k(G)$ is the minimum number of rounds needed for $k$ cops to capture the
robber on $G$ over all possible games in which both players play optimally. In
this paper, we construct a family of graphs having $th_c(G)= \Omega(n^{2/3})$,
establish a sublinear upper bound on the cop throttling number, and show that
the cop throttling number of chordal graphs is $O(\sqrt{n})$. We also introduce
the product cop throttling number $th_c^{\times}(G)$ as a parameter that
minimizes the person-hours used by the cops. This parameter extends the notion
of speed-up that has been studied in the context of parallel processing and
network decontamination. We establish bounds on the product cop throttling
number in terms of the cop throttling number, characterize graphs with low
product cop throttling number, and show that for a chordal graph $G$,
$th_c^{\times}=1+rad(G)$.
