To the classical model of searching for one object out of $n$, we add uncertainty about the parameters $\mathbf{\pi}$ of the distribution of the $n$ objects among the $m$ boxes. Adopting a Bayesian approach, we study the optimal sequential search strategy. For the case $n = 1$, we obtain a generalization of the fundamental result of Blackwell: the strategy which searches at each stage in the "most inviting" box is optimal. This strategy is also optimal for $m = 2$ and arbitrary $n$. However, for $n > 1$ the optimal strategy may be very different from that of the classical model, even when the uncertainty about $\mathbf{\pi}$ is very small.