Zou ( 2006; J. Amer. Statist. Assoc.) proposed the ALASSO method for simultaneous variable selection and estimation of the non‐zero regression parameters, and established its oracle property. In this talk, we provide a precise description of the rate of convergence of the ALASSO estimators of the non‐zero components to the oracle distribution. It is shown that the rate critically depends on the choices of the penalty parameter and the initial estimator, and that confidence intervals (CIs) based on the oracle limit law have poor coverage accuracy. As an alternative, we consider the residual bootstrap method for the ALASSO estimators and show that a naive application of the bootstrap, although consistent, may result in a very slow rate of approximation, with or without studentization. We construct a suitably bias‐adjusted and studentized pivotal version of the ALASSO estimator and show that the bootstrap applied to this modified pivot achieves second‐order correctness, even when the dimension of the non‐zero regression parameters is unbounded. Results from a moderately large simulation study show marked improvement in coverage accuracy for the bootstrap CIs over the oracle based CIs in finite samples.