diff --git a/geo/Geo.tpp b/geo/Geo.tpp
index 529e59c..e03a496 100644
--- a/geo/Geo.tpp
+++ b/geo/Geo.tpp
@@ -1362,11 +1362,12 @@ double withinDist(const Point<T>& p, const XSortedLine<T>& line, double maxDist,
   double euclideanDistUpperBound =
       std::min(maxEuclideanDist, std::min(dist(p, line.rawLine().back().other),
                                           dist(p, line.rawLine().front().p)));
-  double minDist = std::min(
-      std::min(maxDist, distFunc(p, line.rawLine().back().other, maxDist)),
-      distFunc(p, line.rawLine().front().p, maxDist));
+  double minDist = std::min(distFunc(p, line.rawLine().back().other,
+                                     std::numeric_limits<double>::max()),
+                            distFunc(p, line.rawLine().front().p,
+                                     std::numeric_limits<double>::max()));
 
-  auto padding = paddingFunc(euclideanDistUpperBound, minDist,
+  auto padding = paddingFunc(euclideanDistUpperBound, std::min(maxDist, minDist),
                              getBoundingBox(p), line.boundingBox());
 
   // skip irrelevant parts
@@ -1400,8 +1401,8 @@ double withinDist(const Point<T>& p, const XSortedLine<T>& line, double maxDist,
 
     if (euclideanDist < euclideanDistUpperBound) {
       euclideanDistUpperBound = euclideanDist;
-      padding = paddingFunc(euclideanDistUpperBound, minDist, getBoundingBox(p),
-                            line.boundingBox());
+      padding = paddingFunc(euclideanDistUpperBound, std::min(maxDist, minDist),
+                            getBoundingBox(p), line.boundingBox());
     }
   }
 
diff --git a/tests/GeoTestDist.cpp b/tests/GeoTestDist.cpp
index f14b021..03b19d3 100644
--- a/tests/GeoTestDist.cpp
+++ b/tests/GeoTestDist.cpp
@@ -150,9 +150,17 @@ static void testDistWithinRealisticMaxDist() {
        approx(5.5));
   TEST(util::geo::withinDist(XSortedLine<double>(line), point, 10.0), ==,
        approx(5.5));
+  TEST(util::geo::withinDist(XSortedLine<double>(line), point, 5.4), >,
+       5.4);
+  TEST(util::geo::withinDist(XSortedLine<double>(line), point, 5.0), >,
+       5.0);
+  TEST(util::geo::withinDist(XSortedLine<double>(line), point, 1.0), >,
+       1.0);
 
   TEST(util::geo::withinDist(XSortedPolygon<double>(poly), point2, 10.0), ==,
        approx(sqrt(2)));
+  TEST(util::geo::withinDist(XSortedPolygon<double>(poly), point2, 1.0), >,
+       1);
   TEST(util::geo::withinDist(point2, XSortedPolygon<double>(poly), 10.0), ==,
        approx(sqrt(2)));
 
@@ -172,6 +180,12 @@ static void testDistWithinRealisticMaxDist() {
   TEST(util::geo::withinDist(XSortedPolygon<double>(polyWithInner),
                              point, 10.0),
        ==, approx(0.5));
+  TEST(util::geo::withinDist(XSortedPolygon<double>(polyWithInner),
+                             XSortedLine<double>(line2), .2),
+       >, 0.2);
+  TEST(util::geo::withinDist(XSortedPolygon<double>(polyWithInner),
+                             point, .4),
+       >, 0.4);
 
   TEST(util::geo::withinDist(XSortedPolygon<double>(poly2),
                              XSortedPolygon<double>(polyWithInner), 10.0),
@@ -179,6 +193,9 @@ static void testDistWithinRealisticMaxDist() {
   TEST(util::geo::withinDist(XSortedPolygon<double>(polyWithInner),
                              XSortedPolygon<double>(poly2), 10.0),
        ==, approx(0.25));
+  TEST(util::geo::withinDist(XSortedPolygon<double>(polyWithInner),
+                             XSortedPolygon<double>(poly2), .2),
+       >, 0.2);
 }
 
 // _____________________________________________________________________________