Many models of Beyond the Standard Model physics involve heavy colored
fermions. We study models where the new fermions have vector interactions and
examine the connection between electroweak precision measurements and Higgs
production. In particular, for parameters which are allowed by precision
measurements, we show that the gluon fusion Higgs cross section and the Higgs
decay branching ratios must be close to those predicted by the Standard Model.
The models we discuss thus represent scenarios with new physics which will be
extremely difficult to distinguish from the minimal Standard Model. We pay
particular attention to the decoupling properties of the vector fermions.