Fiber-based, flexible pressure-sensing systems have attracted attention recently due to their promising application as electronic skins. Here, a new kind of flexible pressure-sensing device based on a polydimethylsiloxane membrane instrumented with double-twisted smart threads (DTSTs) is reported. DTSTs are made of two conductive threads obtained by coating cotton threads with carbon nanotubes. One thread is coated with a homogeneous thickness of single-walled carbon nanotubes (SWCNTs) to detect the intensity of an applied load and the other is coated with a graded thickness of SWCNTs to identify the position of the load along the thread. The mechanism and capacity of DTSTs to accurately sense an applied load are systematically analyzed. Results demonstrate that the fabricated 1D, 2D, and 3D sensing devices can be used to predict both the intensity and the position of an applied load. The sensors feature high sensitivity (between approximate to 0.1% and 1.56% kPa) and tunable resolution, good cycling resilience (>104 cycles), and a short response time (minimum 2.5 Hz). The presented strategy is a viable alternative for the design of simple, low-cost pressure sensors.