In  Str\o m's (no relation) paper "The Homotopy Category is a Homotopy Category" he proves
that the category of unpointed topological spaces, with Hurewicz fibrations and ordinary cofibrations and homotopy equivalences, is a model category.

Then he has a fairly long section on the pointed case, and his results are not as good:  he restricts to well-pointed spaces, and doesn't get all the model category axioms.

But if $\mathcal{M}$ is a model category, then for any 
object $A\in \mathcal{M}$, the category $A \downarrow \mathcal{M}$ inherits a model category structure in perfectly straightforward way.  

So:  what is going on here?  Did he simply miss an easy extension to the pointed case?
Is it possible that the natural model structure on $A \downarrow \mathcal{M}$ is not the one
he wants (i.e., the received cofibrations, fibrations or weak equivalences differ somehow from pointed cofibrations, fibrations and pointed homotopy equivalences)?