A large number of web databases are only accessible through proprietary form-like interfaces which require users to query the system by entering desired values for a few attributes. A key restriction enforced by such an interface is the top-k output constraint - i.e., when there are a large number of matching tuples, only a few (top-k) of them are preferentially selected and returned by the website, often according to a proprietary ranking function. Since most web database owners set k to be a small value, the top-k output constraint prevents many interesting third-party (e.g., mashup) services from being developed over real-world web databases. In this paper we consider the novel problem of "digging deeper" into such web databases. Our main contribution is the meta-algorithm GetNext that can retrieve the next ranked tuple from the hidden web database using only the restrictive interface of a web database without any prior knowledge of its ranking function. This algorithm can then be called iteratively to retrieve as many top ranked tuples as necessary. We develop principled and efficient algorithms that are based on generating and executing multiple reformulated queries and inferring the next ranked tuple from their returned results. We provide theoretical analysis of our algorithms, as well as extensive experimental results over synthetic and real-world databases that illustrate the effectiveness of our techniques.