Recent interest in new early dark energy (NEDE), a cosmological model with a vacuum energy component decaying in a triggered phase transition around recombination, has been sparked by its impact on the Hubble tension. Previous constraints on the model parameters were derived in a Bayesian framework with Markov-chain Monte Carlo (MCMC) methods. In this work, we instead perform a frequentist analysis using the profile likelihood in order to assess the impact of prior volume effects on the constraints. We constrain the maximal fraction of NEDE fNEDE, finding fNEDE=0.076-0.035+0.040 at 68% CL with our baseline dataset and similar constraints using either data from SPT-3G, ACT or full-shape large-scale structure, showing a preference over ΛCDM even in the absence of a SH0ES prior on H0. While this is stronger evidence for NEDE than obtained with the corresponding Bayesian analysis, our constraints broadly match those obtained by fixing the NEDE trigger mass. Including the SH0ES prior on H0, we obtain fNEDE=0.136-0.026+0.024 at 68% CL. Furthermore, we compare NEDE with the early dark energy (EDE) model, finding similar constraints on the maximal energy density fractions and H0 in the two models. At 68% CL in the NEDE model, we find H0=69.56-1.29+1.16 km s-1 Mpc-1 with our baseline and H0=71.62-0.76+0.78 km s-1 Mpc-1 when including the SH0ES measurement of H0, thus corroborating previous conclusions that the NEDE model provides a considerable alleviation of the H0 tension.