  We present the results of the specific heat and AC magnetic susceptibility
measurements of $CeIr_{1-x}Rh_xIn_5$ for x from 0 to 0.5. As x is increased
from 0 both quantities reflect the competition between two effects. The first
is a suppression of superconductivity below the bulk transition temperature of
T$_c = 0.4$ K, which is due to the pair breaking effect of Rh impurities. The
second is an increase in the volume fraction of the superconducting regions
above T$_c$, which we attribute to defect-induced strain. Analysis of the H-T
phase diagram for CeIrIn$_5$obtained from the bulk probes and resistance
measurements points to the filamentary origin of the inhomogeneous
superconductivity at T$_\rho \approx 1.2$ K, where the resistance drops to
zero. The identical anisotropies in the magnetic field dependence of the
specific heat and the resistance anomalies in CeIrIn$_5$ indicate that the
filamentary superconductivity is intrinsic, involving electrons from the part
of the Fermi surface responsible for bulk superconductivity.
