Convergence and linear dispersion properties in implicit particle codes used in plasma simulation are investigated. Inconsistent spatial smoothing and simplified spatial differencing are shown to be closely related and degrade convergence and, if suitable care is not taken, stability. The convergence and dispersion properties of non-iterated, partially converged solution schemes are calculated. A careful combination of an implicit field solution with extrapolation of particle quantities using a previously calculated electric field heed not degrade linear stability and dispersion characteristics. Even with some degradation of convergence, and with only one pass through the coupled particle and field equations on each time step, code performance can be entirely satisfactory if good stability and dispersion characteristics are preserved.