  We consider a simple extension of the electroweak theory, incorporating one
$SU(2)_L$ doublet of colour-octet scalars with Yukawa couplings satisfying the
principle of minimal flavour violation. Using the HEPfit package, we perform a
global fit to the available data, including all relevant theoretical
constraints, and extract the current bounds on the model parameters. Coloured
scalars with masses below 1.05 TeV are already excluded, provided they are not
fermiophobic. The mass splittings among the different (charged and CP-even and
CP-odd neutral) scalars are restricted to be smaller than 20 GeV. Moreover, for
scalar masses smaller than 1.5 TeV, the Yukawa coupling of the coloured scalar
multiplet to the top quark cannot exceed the one of the SM Higgs doublet by
more than 80%. These conclusions are quite generic and apply in more general
frameworks (without fine tunings). The theoretical requirements of perturbative
unitarity and vacuum stability enforce relevant constraints on the quartic
scalar potential parameters that are not yet experimentally tested.
