Volumetric rendering with custom volume shapes

It took me a week to figure out a problem with a vertex shader not able to interpolate a single float output.
I started with a multi-pass stage that produced a volume from a shape, then fed that volume to a volumetric pass and observed unexplainable artefacts. When flying through a scene and entering a volume the buffer that was clipped by a view frustum's near plane would mangle a default buffer value (set by glClear). Attempts to fix that by playing with glEnable(GL_DEPTH_CLAMP), glDepthRange(-1.0, 1.0) etc did not help.
What did work was switching from a float output to a whole vec3, and calculating depth in a fragment shader. Inefficient, and annoying.