Cosmic Strings with Small Tension

We describe cosmic F--term strings with exponentially small tension which are D3 branes wrapped on deformed $A_3$ singularities. We show that brane instanton effects which can be calculated after a geometric transition give rise to an exponentially small volume for the node on which the D3 branes wrap leading to a string with small tension. We generalize our description to the case of non--Abelian cosmic strings and argue that these strings are stable against monopole--anti monopole pair creation.