On-line arithmetic modules were proposed as a way to explore parallelism in arithmetic operations at digit level. By using serial operators that always receive inputs and compute the outputs from most-significant to least-significant digits, on-line arithmetic makes it possible to overlap all arithmetic operations. However, on-line arithmetic modules have an intrinsic on-line delay that impacts the maximum throughput of networks using these modules. The problem is particularly serious for small precision calculation or deep-pipelined networks. This paper presents a solution to the problem. Results of an actual implementation of the solution for some basic arithmetic operators are shown and demonstrate the benefits of the proposed approach. The developed modules are also tested within the framework of an image processing application.