Bootstrapping results that really bootstrap
A classic result provable by bootstrapping (and applicable to proving real lower bounds) is that in any computational model where we have $TIME(n) \neq TIME(n^c)$ for some constant $c &gt; 1$, we in fact have  $TIME(n) \neq TIME(n^{1+\epsilon})$, for every $\epsilon &gt; 0$.

The idea is that if $TIME(n) = TIME(n^{1+\epsilon})$, we can apply a  padding argument repeatedly to obtain $TIME(n) = TIME(n^c)$ for every constant $c$. You can even use such an argument to slightly improve known time hierarchy theorems in various cases.