diff --git a/src/resolvelib/resolvers.py b/src/resolvelib/resolvers.py
index ecc4dadb..bb4e0dfb 100644
--- a/src/resolvelib/resolvers.py
+++ b/src/resolvelib/resolvers.py
@@ -309,23 +309,30 @@ def _backjump(self, causes: list[RequirementInformation[RT, CT]]) -> bool:
             # Remove the state that triggered backtracking.
             del self._states[-1]
 
-            # Ensure to backtrack to a state that caused the incompatibility
-            incompatible_state = False
+            # Optimistically backtrack to a state that caused the incompatibility
             broken_state = self.state
-            while not incompatible_state:
+            while True:
                 # Retrieve the last candidate pin and known incompatibilities.
                 try:
                     broken_state = self._states.pop()
                     name, candidate = broken_state.mapping.popitem()
                 except (IndexError, KeyError):
                     raise ResolutionImpossible(causes) from None
+
+                # If the current dependencies and the incompatible dependencies
+                # are overlapping then we have found a cause of the incompatibility
                 current_dependencies = {
                     self._p.identify(d)
                     for d in self._p.get_dependencies(candidate)
                 }
-                incompatible_state = not current_dependencies.isdisjoint(
-                    incompatible_deps
-                )
+                if not current_dependencies.isdisjoint(incompatible_deps):
+                    break
+
+                # Fallback: We should not backtrack to the point where
+                # broken_state.mapping is empty, so stop backtracking for
+                # a chance for the resolution to recover
+                if not broken_state.mapping:
+                    break
 
             incompatibilities_from_broken = [
                 (k, list(v.incompatibilities))
diff --git a/tests/functional/python/inputs/case/issue-134.json b/tests/functional/python/inputs/case/issue-134.json
new file mode 100644
index 00000000..c786e604
--- /dev/null
+++ b/tests/functional/python/inputs/case/issue-134.json
@@ -0,0 +1,17 @@
+{
+	"index": "issue-134",
+	"requested": [
+		"pandas<=1.4.0,>=1.3.5",
+		"pystac<=1.8.3,>=1.8.2",
+		"pystac-client<=0.3.3,>=0.3.2",
+		"sat-stac<=0.1.1"
+	],
+	"resolved": {
+		"pandas": "1.3.5",
+		"pystac": "1.8.3",
+		"pystac-client": "0.3.3",
+		"sat-stac": "0.1.1",
+		"python-dateutil": "2.7.5",
+		"requests": "2.31.0"
+	}
+}
diff --git a/tests/functional/python/inputs/index/issue-134.json b/tests/functional/python/inputs/index/issue-134.json
new file mode 100644
index 00000000..bbc4a8bc
--- /dev/null
+++ b/tests/functional/python/inputs/index/issue-134.json
@@ -0,0 +1,66 @@
+{
+    "pandas": {
+        "1.4.0": {
+            "dependencies": [
+                "python-dateutil (>=2.8.1)"
+            ]
+        },
+        "1.3.5": {
+            "dependencies": [
+                "python-dateutil (>=2.7.3)"
+            ]
+        }
+    },
+    "pystac": {
+        "1.8.3": {
+            "dependencies": [
+                "python-dateutil (>=2.7.0)"
+            ]
+        },
+        "1.8.2": {
+            "dependencies": [
+                "python-dateutil (>=2.7.0)"
+            ]
+        }
+    },
+    "pystac-client": {
+        "0.3.3": {
+            "dependencies": [
+                "requests (>=2.25)",
+                "pystac (>=1.4.0)"
+            ]
+        },
+        "0.3.2": {
+            "dependencies": [
+                "requests (>=2.25)",
+                "pystac (~=1.2.0)"
+            ]
+        }
+    },
+    "sat-stac": {
+        "0.1.1": {
+            "dependencies": [
+                "python-dateutil (~=2.7.5)"
+            ]
+        },
+        "0.1.0": {
+            "dependencies": [
+                "requests (~=2.19.1)",
+                "python-dateutil (~=2.7.5)"
+            ]
+        }
+    },
+    "python-dateutil": {
+        "2.9.0": {
+            "dependencies": []
+        },
+        "2.7.5": {
+            "dependencies": []
+        }
+    },
+    "requests": {
+        "2.31.0": {
+            "dependencies": []
+        }
+    }
+}