Abstract: We disclose methods for, devices that implement, and structures produced by 3D printing of insulating and airtight walls using fused deposition modeling printers. Several disclosed methods and features contribute to insulating and airtight walls. These can be used individually or in combination. Structures that reduce or eliminate horizontal surfaces through the use of overlying cantilevered contours can be combined with continuous structures that penetrate through multiple layers, selective overfilling, offset joints and additional extrusions to mitigate leakage routes. Self-supporting closed cell structures can be built that form insulating regions by controlling convective losses.