  It is challenging to explain the tentative 125 GeV Higgs signal in the
Minimal Supersymmetric Standard Model (MSSM) without introducing excessive
fine-tuning, and this motivates the study of non-minimal implementations of low
energy supersymmetry (SUSY). A term \lambda SH_uH_d involving a Standard Model
(SM) singlet state S leads to an additional source for the quartic interaction
raising the mass of the lightest SM-like Higgs. However, in order to achieve
m_h \approx 125 GeV with light stops and small stop mixing, it is necessary for
\lambda \gtrsim 0.7 and consequently \lambda may become non-perturbative before
the unification scale. Moreover, as argued by Barbieri, Hall, et al. low
fine-tuning prefers the region \lambda~1-2, leading to new or non-perturbative
physics involving S below the GUT scale (`\lambda SUSY' models). This raises
the concern that precision gauge coupling unification, the prime piece of
indirect experimental evidence for low energy SUSY, may be upset. Using the
NSVZ exact \beta-function along with well motivated assumptions on the strong
coupling dynamics we show that this is not necessarily the case, but rather
there exist classes of UV completions where the strong-coupling effects can
naturally correct for the present ~3% discrepancy in the two-loop MSSM
unification prediction for \alpha_s. Moreover, we argue that in certain
scenarios a period of strong coupling can also be beneficial for t-b
unification, while maintaining the small to moderate values of tan\beta
preferred by the Higgs mass.
