..And another way, texturing strokes. (Here, in Blender Render).
This texture, at 1024x1024, is going to be used to multiply the alpha value of the stroke. It is white where the stroke is to be opaque, and Black where the stroke is to be transparent.
The left half of the illustration shows the texture.
The right half shows how it splits up when 'Use Tips' is checked.
The blue region is repeated down the stroke, the red region constitutes the tail, and the green region constitutes the head.

In the 'Texture' tab, check 'Use Textures'. In this case, because the main stroke texture is continuous, the 'Spacing Along Stroke' setting is only visible as the length of the taper.

When you hit the button to 'Go to Linestyle Textures Properties', you will be able to adjust
Other than the panels shown here, the settings are at their defaults.. (Image Mapping, not shown here, must be set to 'Repeat')

With some tweaks, (In this case I set a minimum stroke length in the 'Strokes' tab of the Line Style settings to get rid of short strokes).. this is the sort of result..

You can see some segmentation of the stroke due to the repeat spacing.. if you rescaled the bits in the original texture, you would be able to maintain the taper length while bringing the spacing down.