  We have recently reported the first direct calorimetric observation of a
magnetic-field-induced first-order phase transition into a high-field FFLO
superconducting state at the Clogston-Chandrasekar `Pauli' paramagnetic limit
$H_p$ in a 2D superconductor
$\kappa-{\textrm{(BEDT-TTF)}}_2{\textrm{Cu}}{\textrm{(NCS)}}_2$. The high-field
state is both higher entropy and strongly paramagnetic, as thermodynamically
required for the FFLO state. Here we compare our results with theoretical
predictions for the field dependence of the high-field FFLO state in the 2D
limit, revealing tentative evidence for transitions between FFLO states of
differing order parameter. We also present calorimetric evidence for a 1st
order phase transition into the FFLO state for a second 2D organic
superconductor:
${\beta}^{\prime\prime}-{\textrm{(BEDT-TTF)}}_2{\textrm{SF}}_5{\textrm{(CH)}}_2{\textrm{(CF)}}_2{\textrm{(SO)}}_3$.
