Some embodiments of the invention provide a configurable integrated circuit (IC). The configurable IC includes first and second interconnect circuits. The first interconnect circuit has a set of input terminals, a set of output terminals, and several connection schemes for communicatively coupling the input terminal set to the output terminal set. During the operation of the IC, the second connection circuit supplies sets of configuration data to the first interconnect circuit at a particular rate for at least a particular time period. At least two supplied configuration data sets are different and configure the first interconnect circuit to use two different connection schemes that differently couple the input and output terminal sets.