T-pieces (Figure 50) are geometrically opposite of the Magill system: the fresh gas flow inlet is near the subject while the expiratory valve or port is the furthest. E type is a valveless system suitable for spontaneously breathing subjects only. F type is a paediatric valveless system.

Figure 51 shows theoretical inspiratory gas flow during spontaneous breathing in a T-piece system. The inspiratory waveform is a sine wave. Integration of flow (area under the curve) yields volume inspired. This is again divided into gas that enters alveoli (VA) and dead space gas (VD). Superimposed on the graph is the fresh gas flow, which is constant. The area under the straight line of the fresh gas flow is the fresh gas volume delivered into the system. It can be seen that at point A the inspiratory flow exceeds the fresh gas flow. Until that point, excess fresh gas was being deposited in the tubing. After that point, inspiratory flow is supplied in part (the part exceeding fresh gas flow) by gas previously deposited in the tubing. Provided that the roughly triangular area between the fresh gas flow line, the inspiratory curve up to point A, and the y-axis, which is the volume deposited in the large bore tubing, equals the area under the peak inspiratory flow above the fresh gas flow line up to point B (which is the volume of gas drawn from the system in excess of fresh gas flow during that time), no CO2-containing gas will be rebreathed.