We use a combined experimental and computational approach to study the effects of chromosome-nuclear envelope (Chr-NE) attachments on the 3D genome organization of Drosophila melanogaster (fruit fly) salivary gland nuclei. We consider 3 distinct models: a Null model - without specific Chr-NE attachments, a 15-attachment model - with 15 previously known Chr-NE attachments, and a 48-attachment model - with 15 original and 33 recently identified Chr-NE attachments. The radial densities of chromosomes in the models are compared to the densities observed in 100 experimental images of optically sectioned salivary gland nuclei forming "z-stacks." Most of the experimental z-stacks support the Chr-NE 48-attachment model suggesting that as many as 48 chromosome loci with appreciable affinity for the NE are necessary to reproduce the experimentally observed distribution of chromosome density in fruit fly nuclei. Next, we investigate if and how the presence and the number of Chr-NE attachments affect several key characteristics of 3D genome organization: chromosome territories and gene-gene contacts. This analysis leads to novel insight about the possible role of Chr-NE attachments in regulating the genome architecture. Specifically, we find that model nuclei with more numerous Chr-NE attachments form more distinct chromosome territories and their chromosomes intertwine less frequently. Intra-chromosome and intra-arm contacts are more common in model nuclei with Chr-NE attachments compared to the Null model (no specific attachments), while inter-chromosome and inter-arm contacts are less common in nuclei with Chr-NE attachments. We demonstrate that Chr-NE attachments increase the specificity of long-range inter-chromosome and inter-arm contacts. The predicted effects of Chr-NE attachments are rationalized by intuitive volume vs. surface accessibility arguments.