diff --git a/Core/include/Acts/TrackFinding/TrackSelector.hpp b/Core/include/Acts/TrackFinding/TrackSelector.hpp
index 459ab996857..6d938c03085 100644
--- a/Core/include/Acts/TrackFinding/TrackSelector.hpp
+++ b/Core/include/Acts/TrackFinding/TrackSelector.hpp
@@ -80,6 +80,10 @@ class TrackSelector {
     std::size_t maxSharedHits = std::numeric_limits<std::size_t>::max();
     double maxChi2 = inf;
 
+    /// Whether a reference surface is required for the track
+    /// If false, the parameter cuts are not evaluated
+    bool requireReferenceSurface = true;
+
     // Defaults to: no cut
     MeasurementCounter measurementCounter;
 
@@ -439,22 +443,33 @@ bool TrackSelector::isValidTrack(const track_proxy_t& track) const {
 
   const Config& cuts = *cutsPtr;
 
-  return track.hasReferenceSurface() &&
-         within(track.transverseMomentum(), cuts.ptMin, cuts.ptMax) &&
-         (!m_isUnbinned || (within(absEta(), cuts.absEtaMin, cuts.absEtaMax) &&
-                            within(_eta, cuts.etaMin, cuts.etaMax))) &&
-         within(track.phi(), cuts.phiMin, cuts.phiMax) &&
-         within(track.loc0(), cuts.loc0Min, cuts.loc0Max) &&
-         within(track.loc1(), cuts.loc1Min, cuts.loc1Max) &&
-         within(track.time(), cuts.timeMin, cuts.timeMax) &&
-         checkMin(track.nMeasurements(), cuts.minMeasurements) &&
-         checkMax(track.nHoles(), cuts.maxHoles) &&
-         checkMax(track.nOutliers(), cuts.maxOutliers) &&
-         checkMax(track.nHoles() + track.nOutliers(),
-                  cuts.maxHolesAndOutliers) &&
-         checkMax(track.nSharedHits(), cuts.maxSharedHits) &&
-         checkMax(track.chi2(), cuts.maxChi2) &&
-         cuts.measurementCounter.isValidTrack(track);
+  auto parameterCuts = [&]() {
+    return within(track.transverseMomentum(), cuts.ptMin, cuts.ptMax) &&
+           (!m_isUnbinned ||
+            (within(absEta(), cuts.absEtaMin, cuts.absEtaMax) &&
+             within(_eta, cuts.etaMin, cuts.etaMax))) &&
+           within(track.phi(), cuts.phiMin, cuts.phiMax) &&
+           within(track.loc0(), cuts.loc0Min, cuts.loc0Max) &&
+           within(track.loc1(), cuts.loc1Min, cuts.loc1Max) &&
+           within(track.time(), cuts.timeMin, cuts.timeMax);
+  };
+
+  auto trackCuts = [&]() {
+    return checkMin(track.nMeasurements(), cuts.minMeasurements) &&
+           checkMax(track.nHoles(), cuts.maxHoles) &&
+           checkMax(track.nOutliers(), cuts.maxOutliers) &&
+           checkMax(track.nHoles() + track.nOutliers(),
+                    cuts.maxHolesAndOutliers) &&
+           checkMax(track.nSharedHits(), cuts.maxSharedHits) &&
+           checkMax(track.chi2(), cuts.maxChi2) &&
+           cuts.measurementCounter.isValidTrack(track);
+  };
+
+  if (cuts.requireReferenceSurface) {
+    return track.hasReferenceSurface() && parameterCuts() && trackCuts();
+  } else {
+    return trackCuts();
+  }
 }
 
 inline TrackSelector::TrackSelector(
diff --git a/Examples/Python/python/acts/examples/reconstruction.py b/Examples/Python/python/acts/examples/reconstruction.py
index fd02c6bddac..922f5da55fc 100644
--- a/Examples/Python/python/acts/examples/reconstruction.py
+++ b/Examples/Python/python/acts/examples/reconstruction.py
@@ -123,10 +123,42 @@
         "maxSharedHits",
         "maxChi2",
         "nMeasurementsGroupMin",
+        "requireReferenceSurface",
     ],
-    defaults=[(None, None)] * 7 + [None] * 7,
+    defaults=[(None, None)] * 7 + [None] * 8,
 )
 
+
+def trackSelectorDefaultKWArgs(c):
+    """
+    Encapsulate this boilerplate code into a function so different uses do not get out of sync
+    """
+    return acts.examples.defaultKWArgs(
+        loc0Min=c.loc0[0],
+        loc0Max=c.loc0[1],
+        loc1Min=c.loc1[0],
+        loc1Max=c.loc1[1],
+        timeMin=c.time[0],
+        timeMax=c.time[1],
+        phiMin=c.phi[0],
+        phiMax=c.phi[1],
+        etaMin=c.eta[0],
+        etaMax=c.eta[1],
+        absEtaMin=c.absEta[0],
+        absEtaMax=c.absEta[1],
+        ptMin=c.pt[0],
+        ptMax=c.pt[1],
+        minMeasurements=c.nMeasurementsMin,
+        maxHoles=c.maxHoles,
+        maxOutliers=c.maxOutliers,
+        maxHolesAndOutliers=c.maxHolesAndOutliers,
+        maxSharedHits=c.maxSharedHits,
+        maxChi2=c.maxChi2,
+        measurementCounter=c.nMeasurementsGroupMin,
+        requireReferenceSurface=c.requireReferenceSurface,
+    )
+
+
 CkfConfig = namedtuple(
     "CkfConfig",
     [
@@ -1418,32 +1450,10 @@ def addCKFTracks(
             else trackSelectorConfig
         )
     )
+
+    overwriteArgs = dict() if len(tslist) == 1 else dict(absEtaMax=None)
     cutSets = [
-        acts.TrackSelector.Config(
-            **acts.examples.defaultKWArgs(
-                loc0Min=c.loc0[0],
-                loc0Max=c.loc0[1],
-                loc1Min=c.loc1[0],
-                loc1Max=c.loc1[1],
-                timeMin=c.time[0],
-                timeMax=c.time[1],
-                phiMin=c.phi[0],
-                phiMax=c.phi[1],
-                etaMin=c.eta[0],
-                etaMax=c.eta[1],
-                absEtaMin=c.absEta[0],
-                absEtaMax=c.absEta[1] if len(tslist) == 1 else None,
-                ptMin=c.pt[0],
-                ptMax=c.pt[1],
-                minMeasurements=c.nMeasurementsMin,
-                maxHoles=c.maxHoles,
-                maxOutliers=c.maxOutliers,
-                maxHolesAndOutliers=c.maxHolesAndOutliers,
-                maxSharedHits=c.maxSharedHits,
-                maxChi2=c.maxChi2,
-                measurementCounter=c.nMeasurementsGroupMin,
-            )
-        )
+        acts.TrackSelector.Config(trackSelectorDefaultKWArgs(c).update(overwriteArgs))
         for c in tslist
     ]
     if len(tslist) == 0:
@@ -1696,23 +1706,7 @@ def addTrackSelection(
 
     # single cut config for implicit single bin eta configuration
     selectorConfig = acts.TrackSelector.Config(
-        **acts.examples.defaultKWArgs(
-            loc0Min=trackSelectorConfig.loc0[0],
-            loc0Max=trackSelectorConfig.loc0[1],
-            loc1Min=trackSelectorConfig.loc1[0],
-            loc1Max=trackSelectorConfig.loc1[1],
-            timeMin=trackSelectorConfig.time[0],
-            timeMax=trackSelectorConfig.time[1],
-            phiMin=trackSelectorConfig.phi[0],
-            phiMax=trackSelectorConfig.phi[1],
-            etaMin=trackSelectorConfig.eta[0],
-            etaMax=trackSelectorConfig.eta[1],
-            absEtaMin=trackSelectorConfig.absEta[0],
-            absEtaMax=trackSelectorConfig.absEta[1],
-            ptMin=trackSelectorConfig.pt[0],
-            ptMax=trackSelectorConfig.pt[1],
-            minMeasurements=trackSelectorConfig.nMeasurementsMin,
-        )
+        trackSelectorDefaultKWArgs(trackSelectorConfig)
     )
 
     trackSelector = acts.examples.TrackSelectorAlgorithm(
diff --git a/Examples/Python/src/ExampleAlgorithms.cpp b/Examples/Python/src/ExampleAlgorithms.cpp
index 598dde87b99..15e407a651c 100644
--- a/Examples/Python/src/ExampleAlgorithms.cpp
+++ b/Examples/Python/src/ExampleAlgorithms.cpp
@@ -109,6 +109,7 @@ void addExampleAlgorithms(Context& ctx) {
       ACTS_PYTHON_MEMBER(maxSharedHits);
       ACTS_PYTHON_MEMBER(maxChi2);
       ACTS_PYTHON_MEMBER(measurementCounter);
+      ACTS_PYTHON_MEMBER(requireReferenceSurface);
       ACTS_PYTHON_STRUCT_END();
 
       pythonRangeProperty(c, "loc0", &Config::loc0Min, &Config::loc0Max);