diff --git a/GPU/Software/Rasterizer.cpp b/GPU/Software/Rasterizer.cpp
index a9d1950418..7a42ef5198 100644
--- a/GPU/Software/Rasterizer.cpp
+++ b/GPU/Software/Rasterizer.cpp
@@ -1293,8 +1293,11 @@ void DrawRectangle(const VertexData &v0, const VertexData &v1, const BinCoords &
 		}
 
 		// Okay, now move ST to the minX, minY position.
-		rowST += (stx / (float)(SCREEN_SCALE_FACTOR * 2)) * (minX - entireX1 + 1);
-		rowST += (sty / (float)(SCREEN_SCALE_FACTOR * 2)) * (minY - entireY1 + 1);
+		// This is the exact distance from the primitive's edge to the sample point - minX and minY
+		// already sit at the pixel center. The +1 that used to be here was compensating for
+		// TriangleEdge::Start's centerOff being a sixteenth of a pixel short of center.
+		rowST += (stx / (float)(SCREEN_SCALE_FACTOR * 2)) * (minX - entireX1);
+		rowST += (sty / (float)(SCREEN_SCALE_FACTOR * 2)) * (minY - entireY1);
 	}
 
 	// And now what we add to spread out to 4 values.
diff --git a/GPU/Software/TransformUnit.cpp b/GPU/Software/TransformUnit.cpp
index b86f625cdf..8c01ff4247 100644
--- a/GPU/Software/TransformUnit.cpp
+++ b/GPU/Software/TransformUnit.cpp
@@ -176,8 +176,11 @@ static ScreenCoords ClipToScreenInternal(Vec3f scaled, const ClipCoords &coords,
 	// 16 = 0xFFFF / 4095.9375
 	// Round up at 0.625 to the nearest subpixel.
 	static_assert(SCREEN_SCALE_FACTOR == 16, "Currently only supports scale 16");
-	int x = (int)(scaled.x * 16.0f + 0.375f - gstate.getOffsetX16());
-	int y = (int)(scaled.y * 16.0f + 0.375f - gstate.getOffsetY16());
+	// floorf, not a plain (int) cast: the cast truncates toward zero, so once the region offset
+	// pushes the result negative it rounds the opposite way from the positive case - and from the
+	// through-mode path below, which is what made the two disagree by one subpixel.
+	int x = (int)floorf(scaled.x * 16.0f + 0.375f - gstate.getOffsetX16());
+	int y = (int)floorf(scaled.y * 16.0f + 0.375f - gstate.getOffsetY16());
 	return ScreenCoords(x, y, scaled.z);
 }
 
diff --git a/test.py b/test.py
index 35f71dd724..47a6ba2eb6 100755
--- a/test.py
+++ b/test.py
@@ -167,6 +167,7 @@ tests_good = [
   "gpu/displaylist/alignment",
   "gpu/dither/dither",
   "gpu/filtering/mipmaplinear",
+  "gpu/filtering/precisionnearest2d",
   "gpu/filtering/precisionnearest3d",
   "gpu/ge/break",
   "gpu/ge/context",
@@ -424,12 +425,14 @@ tests_next = [
   "gpu/displaylist/state",
   "gpu/filtering/linear",
   "gpu/filtering/nearest",
+  # These two pass with --graphics=software, but still fail on the hardware backends,
+  # so they stay here rather than in tests_good until those match too.
   "gpu/filtering/precisionlinear2d",
   "gpu/filtering/precisionlinear3d",
-  "gpu/filtering/precisionnearest2d",
   "gpu/ge/edramswizzle",
   "gpu/ge/get",
   "gpu/primitives/bezier",
+  # Passes with --graphics=software, still fails on the hardware backends.
   "gpu/primitives/continue",
   "gpu/primitives/immediate",
   "gpu/primitives/lines",