Pregnant women carry a mixture of cell-free DNA fragments from self and fetus (non-self) in their circulation. In recent years multiple independent studies have demonstrated the ability to detect fetal trisomies such as trisomy 21, the cause of Down syndrome, by Next-Generation Sequencing of maternal plasma. The current clinical tests based on this approach show very high sensitivity and specificity, although as yet they have not become the standard diagnostic test. Here we describe improvements to the analysis of the sequencing data by reducing GC bias and better handling of the genomic repeats. We show substantial improvements in the sensitivity of the standard trisomy 21 statistical tests, which we measure by artificially reducing read coverage. We also explore the bias stemming from the natural cleavage of plasma DNA by examining DNA motifs and position specific base distributions. We propose a model to correct this fragmentation bias and observe that incorporating this bias does not lead to any further improvements in the detection of fetal trisomy. The improved bias corrections that we demonstrate in this work can be readily adopted into existing fetal trisomy detection protocols and should also lead to improvements in sub-chromosomal copy number variation detection.