With a slight modifications of Henrik's plot, I was able to obtain the desired effects. I sampled the contours list, inceased the thickness, and increased MaxRecursion. Thanks to all for the almost instantaneous help.
k = Pi/21;
contours = Table[psi, {psi, -Pi, Pi, 2 k}];
contours = Take[contours, {2, -1, 2}];
sl[x, y] := -(Exp[x] Sin[y])/(Exp[2 x] - 2 Exp[x] Cos[y] + 1);
ContourPlot[sl[x, y], {x, -Pi, Pi}, {y, -Pi, Pi},
ContourShading -> None, Contours -> contours, PlotRange -> All,
ContourStyle -> Thickness[.004], PerformanceGoal -> "Quality",
PlotPoints -> 25, MaxRecursion -> 4, ImageSize -> Large]
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