We demonstrate operation of a constant-pressure flowmeter capable of generating and accurately measuring flows as low as 1 × 10 −13 mol/s. Generation of such small flows is accomplished by using a small conductance element with C ≈ 25 nL/s. Accurate measurement then requires both low outgassing materials (< 10 −15 mol/s) and small volume changes (≈ 70 µL). We outline the present flowmeter's construction, detail its operation, and quantify its uncertainty, which is < 1 % over the entire operating range and better than 0.3 % over a majority. In particular, we present an analysis of its hydraulic system, and quantify the shift and uncertainty due to the slightly compressible oil. Finally, we compare our flowmeter against a NIST standard flowmeter, and find agreement to within 0.61 % (k = 2). Future modifications could achieve a k = 2 uncertainty of 0.2 %.