  Advancements in practical single-photon sources (SPS) exhibiting high
brightness and low $g^{(2)}(0)$ have garnered significant interest for their
application in quantum key distribution (QKD). To assess their QKD performance,
it is essential to compare them with the widely employed weak coherent pulses
(WCPs) in the decoy state method. In this work, we analyze the non-decoy
efficient BB84 protocol for an SPS, partially characterising its photon
statistics by its $g^{(2)}(0)$ and mean photon number. We compare it to the
2-decoy efficient BB84 with WCPs within the finite-key analysis framework while
optimizing the parameters of both protocols. Our findings indicate that the
non-decoy SPS with a mean photon number of $\langle n \rangle = 0.5$ and
$g^{(2)}(0) = 3.6\%$ can enhance the secure key generation over the 2-decoy WCP
for block sizes under $4.66 \cdot 10^9$ sent signals ($29$ seconds of
acquisition time) at a channel loss of $10$ dB ($52.5$ km of optical fibre).
Additionally, we demonstrate an increase in the maximum tolerable channel loss
for SPSs with mean photon number $\langle n \rangle \geq 0.0142$ at block sizes
below $10^8$ sent signals ($0.62$ seconds of acquisition time). These results
suggest that SPSs hold potential for key rate enhancement in short-range QKD
networks, though further research is required to evaluate their key generation
capabilities when integrated into the decoy method.
