How to make crossfades inaudible

For years I've noticed crossfades between two wavs don't behave predictably in Reaper (and presumably other DAWs).
Reaper defaults to a curved crossfade which I always assumed was designed to account for the logarithmic scale of loudness so the crossfade was inaudible. Generally this works fine, and in these cases switching to a linear X-fade then creates an audible 'dip' in the edit.
However, I've noticed some crossfades have an audible 'swell' and actually need switching from the default curve to a linear fade to work seamlessly.
I always thought the logarithmic shape was foolproof, but is it programme-dependent?
Certainly I've found particular instruments (e.g. pianos and organs) to be more fussy about the length of the fade, but this is a different issue!
Reaper defaults to a curved crossfade which I always assumed was designed to account for the logarithmic scale of loudness so the crossfade was inaudible. Generally this works fine, and in these cases switching to a linear X-fade then creates an audible 'dip' in the edit.
However, I've noticed some crossfades have an audible 'swell' and actually need switching from the default curve to a linear fade to work seamlessly.
I always thought the logarithmic shape was foolproof, but is it programme-dependent?
Certainly I've found particular instruments (e.g. pianos and organs) to be more fussy about the length of the fade, but this is a different issue!