  We examine a model with multiple scalar fields to see whether it is possible
to reduce the fine- tuning of the SM Higgs mass without introducing low scale
top partners. Our approach may be regarded as a generalization of the condition
proposed by Veltman, who attempted to predict the Higgs mass using the
criterion that the various low energy contributions to the quadratic divergence
of the Higgs mass cancel. Although the Veltman condition predicts the wrong
Higgs mass in the Standard Model, it can still be adapted to extended Higgs
sectors. Furthermore, theories with additional Higgs bosons can lead to
suppressed Yukawa couplings of the top quark to the 125 GeV Higgs, making the
associated one-loop divergence smaller. Here, we review possible extensions of
the Standard Model where the Veltman condition could be realized, and study in
detail one minimal model with two extra scalar fields. For this model and for a
cutoff of 5 TeV, we show that the overall fine-tuning can be considerably
lowered without introducing low-scale Landau poles, albeit the Higgs sector
will be strongly coupled at the cutoff. Models where the top Yukawa coupling is
reduced, in particular, will be within the reach of the upcoming LHC searches.
