  We develop a one-parameter family of static baby Skyrme models that do not
require a potential term to admit topological solitons. This is a novel
property as the standard baby Skyrme model must contain a potential term in
order to have stable soliton solutions, though the Skyrme model does not
require this. Our new models satisfy an energy bound that is linear in terms of
the topological charge and can be saturated in an extreme limit. They also
satisfy a virial theorem that is shared by the Skyrme model. We calculate the
solitons of our new models numerically and observe that their form depends
significantly on the choice of parameter. In one extreme, we find compactons
while at the other there is a scale invariant model in which solitons can be
obtained exactly as solutions to a Bogomolny equation. We provide an initial
investigation into these solitons and compare them with the baby Skyrmions of
other models.
