We investigate a class of actions for lattice QCD with staggered quark
s aimed at reducing the flavour symmetry violations associated with us
ing staggered fermions. These actions replace the gauge field link fie
lds in the quark action with covariantly smeared fields. As such they
are an extension of actions considered by the MILC collaboration. We s
how that such actions systematically reduce flavour symmetry violation
s in the weak coupling Limit. Using the mass splitting between Goldsto
ne and non-Goldstone pions as a measure of flavour symmetry violations
we find that these actions have considerably less flavour symmetry vi
olations than the standard staggered action, and represent an improvem
ent on what can be achieved with the MILC action, on quenched configur
ations with beta = 5.7.