plotting - How to get StreamPlot to draw many hundreds of streamlines?

For artistic reasons, I want to draw an extremely dense StreamPlot with something like a thousand streamlines. I tried setting StreamPoints -> {Automatic, d} where $d$ is a small value specifying the minimum distance between streamlines, but after a point reducing the value of $d$ stops having an effect.

GraphicsColumn[
 StreamPlot[{-1 - x^2 + y, 1 + x - y^2}, {x, -3, 3}, {y, -3, 3}, 
    StreamPoints -> {Automatic, #}, ImageSize -> Medium] & /@ {1, 0.3,
    0.1, 0.03, 0.01}]

The same thing happens when setting StreamPoints -> n for increasing values of $n$, or when manually seeding hundreds of seed points; Mathematica silently refuses to plot any more streamlines.

How can I get around this? Is it possible to plot arbitrarily closely spaced streamlines using StreamPlot?

Update: To clarify, I want to keep the style of the fully-automatic default StreamPlot, which attempts to maintain a uniform spacing between streamlines, and just make it denser. So I don't want to get rid of the minimum distance entirely; I just want to lower it. To save everyone some time, here is what I find unsatisfactory about all the documented settings for StreamPoints.

• None: Obviously no good.


• $n$: Stops having an effect somewhere between 50 and 100.


• Automatic, Coarse, and Fine: Not dense enough.


• {p1, p2, ...} and {{p1, g1}, ...}: See n.


• {spec, d}: d stops having an effect somewhere between 0.2 and 0.1.


• {spec, {dStart, dEnd}}: Strangely, increasing dEnd plots more streamlines. Compare {Automatic, {0.5, 10}} with {Automatic, 0.5} and {Automatic, {0.5, 0.5}}. I don't understand this setting at all.


• {spec, d, len}: When spec is Automatic, len has no effect as far as I can tell. On the other hand, when spec is {p1, p2, ...}, len causes d to be ignored completely.