In cell-free massive multiple-input multiple-output (MIMO) the fluctuations of the channel gain from the access points to a user are large due to the distributed topology of the system. Because of these fluctuations, data decoding schemes that treat the channel as deterministic perform inefficiently. A way to reduce the channel fluctuations is to design a precoding scheme that equalizes the effective channel gain seen by the users. Conjugate beamforming (CB) poorly contributes to harden the effective channel at the users. In this work, we propose a variant of CB dubbed enhanced normalized CB (ECB), in that the precoding vector consists of the conjugate of the channel estimate normalized by its squared norm. For this scheme, we derive an exact closed-form expression for an achievable downlink spectral efficiency (SE), accounting for channel estimation errors, pilot reuse and user's lack of channel state information (CSI), assuming independent Rayleigh fading channels. We also devise an optimal max-min fairness power allocation based only on large-scale fading quantities. ECB greatly boosts the channel hardening enabling the users to reliably decode data relying only on statistical CSI. As the provided effective channel is nearly deterministic, acquiring CSI at the users does not yield a significant gain.