  Benkeser et al. demonstrate how adjustment for baseline covariates in
randomized trials can meaningfully improve precision for a variety of outcome
types. Their findings build on a long history, starting in 1932 with R.A.
Fisher and including more recent endorsements by the U.S. Food and Drug
Administration and the European Medicines Agency. Here, we address an important
practical consideration: *how* to select the adjustment approach -- which
variables and in which form -- to maximize precision, while maintaining Type-I
error control. Balzer et al. previously proposed *Adaptive Prespecification*
within TMLE to flexibly and automatically select, from a prespecified set, the
approach that maximizes empirical efficiency in small trials (N$<$40). To avoid
overfitting with few randomized units, selection was previously limited to
working generalized linear models, adjusting for a single covariate. Now, we
tailor Adaptive Prespecification to trials with many randomized units. Using
$V$-fold cross-validation and the estimated influence curve-squared as the loss
function, we select from an expanded set of candidates, including modern
machine learning methods adjusting for multiple covariates. As assessed in
simulations exploring a variety of data generating processes, our approach
maintains Type-I error control (under the null) and offers substantial gains in
precision -- equivalent to 20-43\% reductions in sample size for the same
statistical power. When applied to real data from ACTG Study 175, we also see
meaningful efficiency improvements overall and within subgroups.
