Yield estimates of fibre in Jute plants (Capsulanes) are usually obtained on the basis of random samples of plants. These estimates are required by the government for the purpose of planning and policy formulation. Due to time and resource constraint, it becomes quite often difficult to compute yield estimates from samples of large size. In this paper an attempt has been made to propose a method based on Gaussian quadrature to estimate the fibre yield from smaller samples. Identification of plants comprising a smaller sample and corresponding weights to be assigned to the yield of plants included in the smaller sample is done with the help of information on auxiliary variables relating to biometrical characteristics (such as plant height and base diameter) of the Jute plants in full sample. Computational experience reveals that the proposed method leads to about 80% reduction in sample size with an absolute percentage error of 1.5%. Performance of the proposed method has been compared with that of simple random sampling on the basis of the values of average absolute percentage error and standard deviation of the estimates of fibre yield. Interestingly, for the proposed method, values of average absolute percentage error as well as standard deviation based on forty samples are found to be smaller than those obtained from simple random sampling scheme. The proposed method is quite general and it can be applied for other crops as well provided information on auxiliary variables relating to yield contributing biometrical characteristics is available.