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A dark energy-like component in the early universe, known as early darkenergy (EDE), is a proposed solution to the Hubble tension. Currently, there isno consensus in the literature as to whether EDE can simultaneously solve theHubble tension and provide an adequate fit to the data from the cosmicmicrowave background (CMB) and large-scale structure of the universe. In thiswork, we deconstruct the current constraints from the Planck CMB and thefull-shape clustering data of the Baryon Oscillation Spectroscopic Survey(BOSS) to understand the origin of different conclusions in the literature. Weuse two different analyses, a grid sampling and a profile likelihood, toinvestigate whether the current constraints suffer from volume effects uponmarginalization and are biased towards some values of the EDE fraction,$f_\mathrm{EDE}$. We find that $f_\mathrm{EDE}$ allowed by the data stronglydepends on the particular choice of the other parameters of the model and thatseveral choices of these parameters prefer larger values of $f_\mathrm{EDE}$than in the Markov Chain Monte Carlo analysis. This suggests that volumeeffects are the reason behind the disagreement in the literature. Motivated bythis, we use a profile likelihood to analyze the EDE model and compute aconfidence interval for $f_\mathrm{EDE}$, finding $f_\mathrm{EDE} = 0.072\pm0.036$ ($68\%$ C.L.). This confidence interval is not subject to volumeeffects; thus, our approach yields more robust constraints on EDE and providesa powerful tool to understand whether EDE is a possible solution to the Hubbletension.

New constraint on Early Dark Energy from Planck and BOSS data using the profile likelihood