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Adjustment for prognostic baseline covariates when estimating treatment effects in randomized trials can reduce bias due to covariate imbalance and yield guaranteed efficiency gain in large-samples. Gains in precision and reductions in finite-sample bias are arguably most important in the resource-limited setting of early-phase trials. Despite their favorable large-sample properties, the utility of covariate-adjusted estimators in early-phase trials is complicated by precision loss due to adjustment for weakly prognostic covariates and type I error rate inflation and undercoverage of asymptotic confidence intervals in finite samples. We propose adjustment for a valid negative control outcomes (NCO), or an auxiliary post-randomization outcome assumed completely unaffected by treatment but correlated with the outcome of interest. We articulate the causal assumptions that permit adjustment for NCOs, describe when NCO adjustment may improve upon adjustment for baseline covariates, illustrate performance and provide practical recommendations regarding model selection and finite-sample variance corrections in early-phase trials using numerical experiments, and demonstrate superior performance of NCO adjustment in the reanalysis of two early-phase vaccine trials in HIV exposed uninfected (HEU) infants. In early-phase studies without knowledge of baseline predictors of outcomes, we advocate for eschewing baseline covariates adjustment in favor of adjustment for NCOs believed to be unaffected by the experimental intervention., Comment: 22 pages, 6 figure, 4 in main text