The objective of this paper is to assess the creep law of natural salt in a small deviatoric stress range. In this range, creep is suspected to be much faster than what is predicted by most constitutive laws used in the cavern and mining industries. Five 2-year, multistage creep tests were performed with creep-testing devices set in a gallery of the Altaussee mine in Austria to take advantage of the very stable temperature and humidity conditions in this salt mine. Each stage was 8-month long. Dead loads were applied, and vertical displacements were measured through gages that had a resolution of 12.5 nm. Loading steps were 0.2, 0.4, and 0.6 MPa, which are much smaller than the loads that are usually applied during creep tests (5–20 MPa). Five salt samples were used: two samples were cored from the Avery Island salt mine in Louisiana, United States; two samples were cored from the Gorleben salt mine in Germany; and one sample was cored from a deep borehole at Hauterives in Drôme, France. During these tests, transient creep is relatively long (6–10 months). Measured steady-state strain rates ( = 10−13–10−12 s−1) are much faster (by 7–8 orders of magnitude) than those extrapolated from relatively high-stress tests (σ = 5–20 MPa). When compared to n = 5 within the high-stress domain for Gorleben and Avery Island salts, a power-law stress exponent within the low-stress domain appears to be close to n = 1. These results suggest that the pressure solution may be the dominant deformation mechanism in the steady-state regime reached by the tested samples and will have important consequences for the computation of caverns or mines behavior. This project was funded by the Solution-Mining Research Institute.