  We study variable time search, a form of quantum search where queries to
different items take different time. Our first result is a new quantum
algorithm that performs variable time search with complexity $O(\sqrt{T}\log
n)$ where $T=\sum_{i=1}^n t_i^2$ with $t_i$ denoting the time to check the
$i$-th item. Our second result is a quantum lower bound of $\Omega(\sqrt{T\log
T})$. Both the algorithm and the lower bound improve over previously known
results by a factor of $\sqrt{\log T}$ but the algorithm is also substantially
simpler than the previously known quantum algorithms.
