Species distribution models are an important tool to predict potential spread of weeds. While recent progress has improved model performance, there is still concern about the validity of such models, especially when applied to novel geographical regions or climates. This study investigates how different sets of variables influence predicted distributions, considering several measures of model performance and how extrapolation to novel geographical regions may affect results. Potential distributions of three new weeds in New Zealand (Archontophoenix cunninghamiana, Psidium guajava and Schefflera actinophylla) are modelled, by training a model based on global data from native and introduced ranges and projecting it to New Zealand, using Maxent. For each species, four models were calibrated: first with a full set of 19 bioclimatic variables, then with a customised set with selection based on analysis of response curves and finally with two reduced sets of uncorrelated variables. Although AUC across all models was very high (AUC ≥ 0.9), correlations between models ranged between 0.27 and 0.98. Inclusion of all variables predicted larger areas to be suitable in the projected region, with highly unlikely predictions in some areas, especially where bioclimatic variables showed values outside the range of the training data (new environments). Conversely, minimal extrapolation and more realistic predictions of weed distributions were obtained from models including a customised set of variables, and even more so from models including only a reduced set of variables. This study shows that careful selection of variables and investigation into extrapolation are vital in generating more realistic predictions of weed distributions.