diff --git a/gap/matrix/classical.gi b/gap/matrix/classical.gi
index 5ce5f90a..86484381 100644
--- a/gap/matrix/classical.gi
+++ b/gap/matrix/classical.gi
@@ -1136,6 +1136,27 @@ function(recognise)
     fi;
 end);
 
+BindRecogMethod("FindHomMethodsClassical", "Degree2SL",
+"tests whether a degree-2 group contains SL",
+function(recognise)
+    if recognise.d <> 2 then
+        return NeverApplicable;
+    fi;
+
+    if RECOG.IsThisSL2Natural(GeneratorsOfGroup(recognise.grp),
+                              recognise.field) then
+        recognise.isGeneric := false;
+        recognise.isReducible := false;
+        recognise.isNotExt := true;
+        recognise.isSLContained := true;
+        recognise.isSpContained := true;
+        Info(InfoClassical,2,"The group contains SL(2, ", recognise.q, ");");
+        return Success;
+    fi;
+
+    return TemporaryFailure;
+end);
+
 ## Main function to test whether group contains SL
 BindRecogMethod("FindHomMethodsClassical", "IsSLContained",
 "tests whether group contains SL",
@@ -2436,6 +2457,8 @@ AddMethod(ClassicalMethDb, FindHomMethodsClassical.NonGenericOrthogonalMinus, 14
 
 AddMethod(ClassicalMethDb, FindHomMethodsClassical.NonGenericOrthogonalCircle, 15);
 
+AddMethod(ClassicalMethDb, FindHomMethodsClassical.Degree2SL, 16);
+
 AddMethod(ClassicalMethDb, FindHomMethodsClassical.IsSLContained, 16);
 
 AddMethod(ClassicalMethDb, FindHomMethodsClassical.IsSpContained, 17);
diff --git a/gap/projective/classicalnatural.gi b/gap/projective/classicalnatural.gi
index b9040e00..c89e5c5b 100644
--- a/gap/projective/classicalnatural.gi
+++ b/gap/projective/classicalnatural.gi
@@ -854,17 +854,10 @@ function(ri)
   RECOG.SetPseudoRandomStamp(g,"ClassicalNatural");
 
   # First check whether we are applicable:
-  if d = 2 then
-      if not RECOG.IsThisSL2Natural(GeneratorsOfGroup(g),f) then
-          Info(InfoRecog,2,"ClassicalNatural: Is not PSL_2.");
-          return TemporaryFailure; # FIXME: TemporaryFailure here really correct?
-      fi;
-  else
-      classical := RecogniseClassical(g);
-      if classical.isSLContained <> true then
-          Info(InfoRecog,2,"ClassicalNatural: Is not PSL.");
-          return TemporaryFailure; # FIXME: TemporaryFailure here really correct?
-      fi;
+  classical := RecogniseClassical(g);
+  if classical.isSLContained <> true then
+      Info(InfoRecog,2,"ClassicalNatural: Is not PSL.");
+      return TemporaryFailure; # FIXME: TemporaryFailure here really correct?
   fi;
 
   # Now get rid of nasty determinants:
diff --git a/tst/working/quick/classical.tst b/tst/working/quick/classical.tst
index 3c20c827..84cfecab 100644
--- a/tst/working/quick/classical.tst
+++ b/tst/working/quick/classical.tst
@@ -18,3 +18,11 @@ gap> SetX(G, G, function(g,h)
 >   return gh = false or (IsEqualProjective(gh[1], g) and IsEqualProjective(gh[2], h));
 > end);
 [ true ]
+
+# issue #345: degree-2 linear groups should still report containment of SL
+gap> ri := RecogniseClassical(SL(2,37));;
+gap> ri.isSLContained;
+true
+gap> ri := RecogniseClassical(SL(2,25));;
+gap> ri.isSLContained;
+true