This paper proposes a local processors-assisted structure (LPs-AS) for cell-free massive multiple-input multiple-output (CF-mMIMO) systems, consisting of a central processor (CP), several access points (APs), and some local processors (LPs). Each LP is connected to the CP and a subset of APs and is used as a precoding unit in downlink (DL). This proposed LPs-AS enables us to implement DL precoders with a semi-distributed approach. In our proposed semi-distributed implementation (SDI), we design precoders at the LPs. This approach differs from centralized implementation (CI) where the precoders are implemented at the CP and distributed implementation (DI) where the precoders are designed at the APs. We evaluate LPs-AS in terms of spectral efficiency (SE) and analytically derive its achievable SE. Furthermore, we propose a power control algorithm to maximize its sum SE, compute the computational complexity (CC) of its minimum mean square error (MMSE) precoders, and compare this CC with its counterpart in CI and DI. Numerical results demonstrate that employing an optimal number of LPs (between 2 and 4) in our proposed LPs-AS, not only enables us to design DL precoders with significantly low CC but also results in an efficient SDI that effectively addresses the problem of low SE in DI.