We consider the classical setting of private information retrieval (PIR), where a user (retriever) wishes to retrieve one out of M messages that are replicated across N distributed databases. Different from the classical setting, here we consider the case where the retriever is constrained in its access to the databases. In particular, the ratios of the lengths of the answer strings that the retriever can get from the databases are fixed and given. This may happen, for instance, if the capacities (bandwidths) of the links between the user and the databases are different. We show that, in certain cases, despite the forced asymmetry in accessing the databases, unconstrained PIR capacity can be achieved. We also show that, if the access constraints are too asymmetric, then the resulting PIR capacity is strictly smaller than the unconstrained capacity.