Compact numerical schemes for high-order spatial differencing and integration are planned to be incorporated into a non-hydrostatic semi-Lagrangian dynamical core under development at NCEP as part of the multi-institution Weather Research and Forecasting (WRF) project. Since the schemes require recursive operations along entire lines of one dimension, they should be implemented with algorithms carefully devised not to impair their performance seriously. We tested three methods which feature different parallelization strategies for the recursive components, all of which are intended to be computationally efficient. The three methods differ significantly in their handling of communication. We describe these implementations, their motivations and limitations, and their actual computational performance over domains of various sizes.