A *straight *set is an equivariant set which is equivariantly isomorphic to a disjiont union of sets of the form . A straight semigroup is an equivariant semigroup whose universe is a straight set. We raise the following:

**Question 1: **is every equivariant, orbit-finite semigroup an image of some orbit-finite, straight semigroup under an equivariant mapping?

We show some simple preliminary observations towards the above question.