IN ECONOMETRICS, ALMOST ALL LARGE MODELS AND MANY MEDIUM-SIZED MODELS HAVE A NUMBER OF PREDETERMINED VARIABLES EXCEEDING THE NUMBER OF OBSERVATIONS. THIS PROBLEM IS NOT CONFINED TO TWO-STAGE LEAST SQUARES ESTIMATION. FULL INFORMATION METHODS SUCH AS THREE-STAGE LEAST SQUARES ANALYSIS AND LINEARIZED MAXIMUM-LIKELIHOOD TECHNIQUES USE TWO-STAGE LEAST SQUARES ESTIMATES AS BASIC INGREDIENTS AND ARE INAPPLICABLE WHEN TWO-STAGE LEAST SQUARES ANALYSIS IS NOT APPROPRIATE. VARIOUS ATTEMPTS TO SOLVE PROBLEMS ASSOCIATED WITH UNDERSIZED SAMPLES ARE REVIEWED, AND A CLASS OF ESTIMATORS FOR UNDERSIZED SAMPLES IS DEVELOPED. CONSIDERATION IS GIVEN TO ASYMPTOTIC VARIANCES AND COVARIANCES. FURTHER INFORMATION ON ESTIMATION PROCEDURES IS APPENDED. SUPPORTING EQUATIIONS ARE INCLUDED. (DEP)