diff --git a/eeschema/sch_pin.cpp b/eeschema/sch_pin.cpp
index 19f044395b..505da44878 100644
--- a/eeschema/sch_pin.cpp
+++ b/eeschema/sch_pin.cpp
@@ -317,6 +317,10 @@ const EDA_RECT SCH_PIN::GetBoundingBox() const
 
 bool SCH_PIN::HitTest( const wxPoint& aPosition, int aAccuracy ) const
 {
+    // When looking for an "exact" hit aAccuracy will be 0 which works poorly if the pin has
+    // no pin number or name.  Give it a floor.
+    aAccuracy = std::max( aAccuracy, GetPenWidth() );
+
     EDA_RECT rect = GetBoundingBox();
     return rect.Inflate( aAccuracy ).Contains( aPosition );
 }
diff --git a/pcbnew/zone.cpp b/pcbnew/zone.cpp
index 26fcaff94b..3a1918bf4b 100644
--- a/pcbnew/zone.cpp
+++ b/pcbnew/zone.cpp
@@ -399,8 +399,8 @@ void ZONE::BuildHashValue( PCB_LAYER_ID aLayer )
 
 bool ZONE::HitTest( const wxPoint& aPosition, int aAccuracy ) const
 {
-    // Normally accuracy is zoom-relative, but at high zooms zones can be too hard to select
-    // so we provide a minimum.
+    // When looking for an "exact" hit aAccuracy will be 0 which works poorly for very thin
+    // lines.  Give it a floor.
     int accuracy = std::max( aAccuracy, Millimeter2iu( 0.1 ) );
 
     return HitTestForCorner( aPosition, accuracy * 2 ) || HitTestForEdge( aPosition, accuracy );