A mini-curve is the minimal information you need to determine the effectiveness of a given insulin dose. It consists minimally of 3 blood glucose readings: one reading at shot time, another at peak time, a third at the next shot time. For this to be informative, you must first have done a few 12-hour curves to know the typical peak time of the particular insulin in the particular patient.
Another source recommends four readings for a mini-curve, the extra reading between peak and final shot determines how well the insulin is controlling blood glucose after peak.
The ideal (and therefore unattainable) curve, according to Dr. Deborah Greco, is a dip from the highest blood glucose level (just at shot time, down to a nadir at peak time, and back up again at the next shot time. If you know when that peak time is, you should be able to capture the glucose difference, the difference between highest and lowest BG level, using a mini-curve.
Dr. Greco recommends a glucose difference under 100 mg/dl for dogs, and under 150 mg/dl for cats. In international units, that's 5.6 mmol/L for dogs, 8.2 mmol/L for cats.