This paper investigates power allocation strategies for cell-free massive MIMO (CF-mMIMO) systems based on new secure MIMO precoding methods, through a revisited secrecy energy efficiency (SEE) metric. We extend secure projectionbased precoding with unconstrained power per access point (AP) to locally and globally constrained per-AP power schemes. Our analysis reveals that secrecy degrades under local power constraints due to a loss of orthogonality to the eavesdropper’s (referred as Eve) channel, whereas perfect secrecy is achievable with globally constrained power allocation, albeit at the cost of reduced transmit power. Furthermore, we revisit the conventional secrecy rate metric to better reflect the legitimate user’s (referred as Bob) achievable rate while ensuring that Eve remains unable to decode the confidential message. This refined secrecy rate definition enables a comprehensive joint analysis of secrecy performance and power consumption, leading to a relevant formulation of SEE. Theoretical findings are validated through simulations, which compare the proposed power allocation strategies and precoders against artificial noise injection scheme and the conventional unconstrained power per-AP configuration.