Nonlinear principal component analysis (NLPCA) by autoassociate feedforward neural networks with 3 hidden layers of neurons has recently been applied to analyze a number of meteorological/oceanographic datasets. However, many of these datasets, especially climate datasets, tend to be relatively short and noisy. Under these conditions, NLPCA with its large number of parameters and great flexibility could easily lead to overfitting, i.e. fitting to noise in the dataset. We found that by trimming the NLPCA network from 3 to 2 hidden layers, and eliminating the bias parameters from the bottleneck and output layers, a simpler NLPCA model results, which greatly alleviates the overfitting problem and the non-uniqueness problem associated with the nonlinear principal component. This new model is applied to several datasets-- the Lorenz (1963) chaotic system, the tropical Pacific sea surface temperatures, and the stratospheric zonal winds (with the quasi-biennial oscillation phenomenon).