The precise structural understanding of uncountably categorical theories given by the Baldwin-Lachlan theorem is known to fail in continuous logic in the context of inseparably categorical theories. The primary obstacle is the absence of strongly minimal sets in some inseparably categorical theories. We will develop the concept of strongly minimal sets in continuous logic and discuss some common conditions under which they are present in an ω-stable metric theory. Finally we will examine the extent to which we recover the Baldwin-Lachlan theorem in the presence of strongly minimal sets.