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 superiority of simple-average combinations, we propose LASSO-based procedures that select and shrink toward equal combining weights. We then provide an empirical assessment of the performance of our "egalitarian LASSO" procedures. The results indicate that simple averages are highly competitive, and that although out-of-sample RMSE improvements on simple averages are possible in principle using our methods, they are hard to achieve in real time, due to the intrinsic difficulty of small-sample real-time cross validation of the LASSO tuning parameter. We therefore propose alternative direct combination procedures, most notably "best average" combination, motivated by the structure of egalitarian LASSO and the lessons learned, which do not require choice of a tuning parameter yet outperform simple averages.