Abstract: Paul Larson proved that under Martin's axiom and large continuum there are no Laver ideals over aleph_1. He asked about weakly Laver ideals under some forcing axiom. We shall address two issues: 1. Under Martin's axiom and the continuum is above aleph_2, there are no weakly Laver ideals over aleph_1.. 2. Under Baumgartner's axiom, the parallel of Larson's theorem holds for ideals over aleph_2.