  We present combined photometric and spectroscopic analyses of the southern
binary star PU Pup. High-resolution spectra of this system were taken at the
University of Canterbury Mt. John Observatory in the years 2008 and again in
2014-15. We find the light contribution of the secondary component to be only
$\sim$2\% of the total light of the system in optical wavelengths, resulting in
a single-lined spectroscopic binary. Recent TESS data revealed grazing eclipses
within the light minima, though the tidal distortion, examined also from
HIPPARCOS data, remains the predominating light curve effect. Our model shows
PU Pup to have the more massive primary relatively close to filling its Roche
lobe. PU Pup is thus approaching the rare `fast phase' of interactive (Case B)
evolution. Our adopted absolute parameters are as follows: $M_1$ = 4.10
($\pm$0.20) M$_{\odot}$, $M_2$ = 0.65 ($\pm$0.05) M$_{\odot}$, $R_{1}$ = 6.60
($\pm$0.30) R$_{\odot}$, $R_2$ = 0.90 ($\pm$0.10) R$_{\odot}$; $T_{1}$ = 11500
($\pm$500) K, $T_{2}$ = 5000 ($\pm$350) K; photometric distance = 186 ($\pm$20)
pc, age = 170 ($\pm$20) My. The less-massive secondary component is found to be
significantly oversized and overluminous compared to standard Main Sequence
models. We discuss this discrepancy referring to heating from the reflection
effect.
