Padding Between Upper and Lower Beams?

[Champion James]

Hello,

I overrode the default beam thickness, as the beams looked a tad scrawny to me. 
 
At 0.7 staff spaces, they look much better to my taste.  However, increasing 
the 
thickness makes the lower beams of 16th and 32nd notes run into the upper 
beams, 
creating the appearance of a single, massive beam.  I scoured the IR manual 
looking for anything that might set the padding between the upper and lower 
beams and/or set the position of lower beams, to no avail.  Increasing the stem 
length does not seem to have any affect.  The following code block demonstrates 
the issue:

% begin code
\version "2.14.0"

data = {f8 f f16 f f f f32 f f f f f f f }

\score {
  \relative c' {
    f4^\markup {Default beams}
    \data
    \override Beam #'beam-thickness = #0.7
    f4^\markup {Thicker beams collide}
    \data
  }
}

% end code

Anyway to ensure padding between the beam levels, or to shift the lower beams 
closer to the note heads?

Thanks in advance for any and all help,

Champion James