Measurements of the specific heat have been made on three samples of dysprosium aluminum garnet in the critical point region of 2.5°K, using large optical‐quality single crystals and temperature steps down to 50 &mgr;deg. The results for all three samples were very similar but they could not be fitted unambiguously to any of the presently proposed singular functions. In all cases, rounded maxima 2 to 3 mdeg wide were found, with peak values between 4.2 and 5.1R. Below these maxima, the results could be fitted to simple laws of the formC=A_ln |T−TN−| +B_, but above the maxima a logarithmic form could only be fitted by choosingTN+more than 5×10−3°K higher thanTN−. Even then the agreement was not very good, and an apparently better fit could be obtained using the law of the formC=A′(T−TN)−&agr;+B′ withTN+=TN−and &agr;=0.31±0.02. This value of &agr; would be considerably larger than predicted by any of the present theories. These experiments suggest that small broadening effects present even in apparently homogeneous samples can lead to considerable uncertainties in the analysis of critical‐point behavior.