  Theoretical predictions for the core helium burning phase of stellar
evolution are highly sensitive to the uncertain treatment of mixing at
convective boundaries. In the last few years, interest in constraining the
uncertain structure of their deep interiors has been renewed by insights from
asteroseismology. Recently, Spruit (2015) proposed a limit for the rate of
growth of helium-burning convective cores based on the higher buoyancy of
material ingested from outside the convective core. In this paper we test the
implications of such a limit for stellar models with a range of initial mass
and metallicity. We find that the constraint on mixing beyond the Schwarzschild
boundary has a significant effect on the evolution late in core helium burning,
when core breathing pulses occur and the ingestion rate of helium is fastest.
Ordinarily, core breathing pulses prolong the core helium burning lifetime to
such an extent that models are at odds with observations of globular cluster
populations. Across a wide range of initial stellar masses ($0.83 \leq
M/\text{M}_\odot \leq 5$), applying the Spruit constraint reduces the core
helium burning lifetime because core breathing pulses are either avoided or
their number and severity reduced. The constraint suggested by Spruit therefore
helps to resolve significant discrepancies between observations and theoretical
predictions. Specifically, we find improved agreement for $R_2$, the observed
ratio of asymptotic giant branch to horizontal branch stars in globular
clusters; the luminosity difference between these two groups; and in
asteroseismology, the mixed-mode period spacing detected in red clump stars in
the \textit{Kepler} field.
