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Motivated by Hadwiger's conjecture, we study the problem of finding thedensest possible $t$-vertex minor in graphs of average degree at least $t-1$.We show that if $G$ has average degree at least $t-1$, it contains a minor on$t$ vertices with at least $(\sqrt{2}-1-o(1))\binom{t}{2}$ edges. We show thatthis cannot be improved beyond $\left(\frac{3}{4}+o(1)\right)\binom{t}{2}$.Finally, for $t\leq 6$ we exactly determine the number of edges we areguaranteed to find in the densest $t$-vertex minor in graphs of average degreeat least $t-1$.

Finding dense minors using average degree