Despite the clear success of forecast combination in many economic environments, several important issues remain incompletely resolved. The issues relate to selection of the set of forecasts to combine, and whether some form of additional regularization (e.g., shrinkage) is desirable. Against this background, and also considering the frequently-found good performance of simple-average combinations, we propose a LASSO-based procedure that sets some combining weights to zero and shrinks the survivors toward equality (“partially-egalitarian LASSO”). Ex-post analysis reveals that the optimal solution has a very simple form: The vast majority of forecasters should be discarded, and the remainder should be averaged. We therefore propose and explore direct subset-averaging procedures motivated by the structure of partially-egalitarian LASSO and the lessons learned, which, unlike LASSO, do not require choice of a tuning parameter. Intriguingly, in an application to the European Central Bank Survey of Professional Forecasters, our procedures outperform simple average and median forecasts – indeed they perform approximately as well as the ex-post best forecaster.