High-precision measurements of the Nusselt number Nu for Rayleigh-B6nard (RB) convection have been made in rectangular cells of water (Prandtl number Pr ≈ 5 and 7) with aspect ratios (F~, Fy) varying between (1, 0.3) and (20.8, 6.3). For each cell the data cover a range of a little over a decade of Rayleigh number Ra and for all cells they jointly span the range 6x105 〈 Ra 〈1011. The two implicit equations of the Grossmann-Lohse (GL) model together with the empirical finite conductivity cor- rection factorf(X) were fitted to obtain estimates of Nu∞ in the presence of perfectly conducting plates, and the obtained Nu∞ is independent of the cells' aspect ratios. A combination of two-power-law, Nu∞= O.025Ra0.357+O.525Ra0.168, can be used to de- scribe Nu∞(Ra). The fitted exponents 0.357 and 0.168 are respectively close to the predictions 1/3 and 1/5 of the 11μ. and 1Vμ re- gimes of the GL model. Furthermore, a clear transition from the II. regime to the IVμ regime with increasing Ra is revealed.