Carry chains facilitate the implementation of adders and improve the performance of arithmetic circuits in FPGAs. The last version of the commonly used open-source Verilog-to-Routing (VTR) CAD flow now enables modelling carry chains in FPGA architectures. However, one of the shortcomings of the existing flow lies in its inability to identify arithmetic operations when described as gate-level circuits. Moreover, the VTR flow squanders most of the LUTs preceding the chain logic. This paper focuses on these two problems and proposes preprocessing the circuit before technology mapping to allow for a more efficient use of carry chains. The first proposed method maps logic on the carry chains for circuits expressed using a gate-level description. On average, it identifies about 30% more meaningful full adders than the existing tool flow operating on the RTL descriptions. Area is thus improved by up to 15% with an average of 6% for almost no delay penalty. Secondly, we increase the use of the LUTs preceding the chain logic by a factor 2 on average. This reduces delay (up to 9%) and area (up to 2%), compared to the existing VTR flow. The new approach is independent of the specific carry-chain architecture and can be generically adapted to any FPGA with built-in hardened adders.