A decade ago, Pointwise Circumscription was proposed as a tool for formalizing
common sense. In this paper, we revisit some of its uses and examine
some cases in which it does not yield the intended behavior.
Specifically, we explore the cases in which unsatisfiability may result from
the presence of multiple minimal models (for McCarthy's Circumscription).
Then, we present a form of circumscription, called
Point-Sensitive Circumscription,
that is a generalization of McCarthy's
Circumscription and Lifschitz's Generalized Pointwise Circumscription.
We illustrate how 
Point-Sensitive Circumscription handles these cases without losing
the control over selective fine-grained variance of predicates and functions.
Last, we compare the two tools and their potential uses in formalizing
Theories of Action.