It is widely believed that existing electroweak data requires a Standard Model (SM) Higgs to be light, while electroweak and flavour physics constraints require other scalars charged under the SM gauge couplings to be heavy. New Higgs-like scalars that are also colour octets -- well-motivated in the sense that they arise in models having approximate custodial symmetry and minimal flavour violation -- provide counter-examples to both of these statements since the scalars can be all simultaneously light (~ 100 GeV} or heavy (~ 1 TeV}, without running afoul of direct searches and electroweak precision measurements.