We introduce correlated growth into a restricted solid on solid model (RSOS), a stochastic deposition model with a constraint on neighboring height differences. A two-dimensional lattice model is used in which particles are deposited via horizontal Levy flight steps with a step length distribution exponent f. Though RSOS is in the same universality class as ballistic deposition for uncorrelated deposition, it appears to depart from it for strong correlations. For f= 1, the short-range limit is reached and both exponents fl and X, which describe the dependence of surface width on time and strip length, tend to 1. For f > 1 we retreat to an enhanced algorithm, searching for growth sites which become excessively rare. We find an unusual short-time dependence, but g still tends to 1. The number of growth sites G shows saturation for f< 1, while for f~> 1 we observe G/L ~ 0 as the strip length L increases. Finally, we test directly the relationship of noise-noise correlation strength to f, and find that a direct comparison between correlated growth models and theoretical predictions for growth with correlated noise is so far unjustified.