In conventional FORC (First Order Reversal Curve) analysis of a magnetic system, reversible and low-coercivity irreversible materials are treated as being qualitatively different: the FORC distribution shows low-coercivity materials but completely hides reversible (zero-coercivity) ones. This distinction is artificial – as the coercivity approaches zero, the physical properties of an irreversible material change smoothly into those of a reversible material. We have developed a method (called FORC+, implemented in free software at http://MagVis.org) for displaying the reversible properties of a system (a reversible switching-field distribution, R-SFD) together with the irreversible ones (the usual FORC distribution), so that there is no sudden discontinuity in the display when the coercivity becomes zero. We will define a “FORC+ dataset” to include the usual FORC distribution, the R-SFD, the saturation magnetization, and what we will call the “lost hysteron distribution” (LHD) such that no information is lost – the original FORC curves can be exactly recovered from the FORC+ dataset. We also give an example of the application of FORC+ to real data – it uses a novel complementary-color display that minimizes the need for smoothing. In systems which switch suddenly (thus having sharp structures in the FORC distribution) direct display of un-smoothed raw data allows visualization of sharp structures that would be washed out in a conventional smoothed FORC display.