  We test the hypothesis that in models with an explicit breaking of Lorentz
invariance (LIV models) the problem with the cosmological constant may, if not
already be solved, then at least may partially be mitigated by improving its UV
behaviour. Certain class of noncommutative models that have a well defined dual
momentum space geometry and in addition set up a suitable frame for developing
the appropriate DSR models are also subject to the same test.
