  We show that over any ring, the double Ext-orthogonal class to all flat
Mittag-Leffler modules contains all countable direct limits of flat
Mittag-Leffler modules. If the ring is countable, then the double orthogonal
class consists precisely of all flat modules and we deduce, using a recent
result of \v{S}aroch and Trlifaj, that the class of flat Mittag-Leffler modules
is not precovering in Mod-R unless R is right perfect.
