  We analyze several ``strong meager'' properties for filters on the natural
numbers between the classical Baire property and a filter being $F_\sigma$. Two
such properties have been studied by Talagrand and a few more combinatorial
ones are investigated. In particular, we define the notion of a P$^+$-filter, a
generalization of the traditional concept of P-filter, and prove the existence
of a non-meager P$^+$-filter. Our motivation lies in understanding the
structure of filters generated by complements of members of a maximal almost
disjoint family.
