Sometimes we can make assumptions without loss of generality. Sometime we restrict the problem a lot, sometimes just a little - it is with hardly any loss of generality. What is the jargon for the later two? "restrictive assumption" and "soft assumption"?
I'll give an example:
To rectify this, we make $\mathbb D$ a bounded subset $\mathbb D\subset\mathbb R$, which is a .... assumption.
I want to say that it important to make this assumption for mathematical reasons, but does not make much difference for the results (because we can still make $\mathbb D$ as large as we need).
I think the terms are "weak assumption" for a non-restrictive assumption close to "without loss of generality" and "strong assumption" for restrictive assumptions.