Dynamic Circuit Specialisation (DCS) is a technique that uses the reconfigurability of an FPGA to optimise a circuit during run-time, thus achieving higher performance and lower resource cost. However, run-time reconfiguration causes transitional effects that form an important problem for DCS. Because of these, the DCS circuit cannot be used while it is being reconfigured. This limits the usability of DCS for streaming applications and other applications that cannot tolerate downtime. For other applications, this results in a loss of performance. In this paper, we present a technique to perform partial reconfiguration for DCS without transitional effects, thus allowing the circuit to remain fully functional at all times. The proposed method performs DCS by reconfiguring only LookUp Tables of the FPGA and does not require changes to the configuration architecture of the FPGA. The approach was tested and evaluated on current Xilinx FPGAs.