diff --git a/src/backend/optimizer/path/equivclass.c b/src/backend/optimizer/path/equivclass.c
index 7997f50c18d..a225414c970 100644
--- a/src/backend/optimizer/path/equivclass.c
+++ b/src/backend/optimizer/path/equivclass.c
@@ -27,6 +27,7 @@
 #include "optimizer/paths.h"
 #include "optimizer/planmain.h"
 #include "optimizer/prep.h"
+#include "optimizer/restrictinfo.h"
 #include "optimizer/var.h"
 #include "utils/lsyscache.h"
 
@@ -71,8 +72,14 @@ static bool reconsider_full_join_clause(PlannerInfo *root,
  *	  any delay by an outer join, so its two sides can be considered equal
  *	  anywhere they are both computable; moreover that equality can be
  *	  extended transitively.  Record this knowledge in the EquivalenceClass
- *	  data structure.  Returns TRUE if successful, FALSE if not (in which
- *	  case caller should treat the clause as ordinary, not an equivalence).
+ *	  data structure, if applicable.  Returns TRUE if successful, FALSE if not
+ *	  (in which case caller should treat the clause as ordinary, not an
+ *	  equivalence).
+ *
+ * In some cases, although we cannot convert a clause into EquivalenceClass
+ * knowledge, we can still modify it to a more useful form than the original.
+ * Then, *p_restrictinfo will be replaced by a new RestrictInfo, which is what
+ * the caller should use for further processing.
  *
  * If below_outer_join is true, then the clause was found below the nullable
  * side of an outer join, so its sides might validly be both NULL rather than
@@ -104,9 +111,11 @@ static bool reconsider_full_join_clause(PlannerInfo *root,
  * memory context.
  */
 bool
-process_equivalence(PlannerInfo *root, RestrictInfo *restrictinfo,
+process_equivalence(PlannerInfo *root,
+					RestrictInfo **p_restrictinfo,
 					bool below_outer_join)
 {
+	RestrictInfo *restrictinfo = *p_restrictinfo;
 	Expr	   *clause = restrictinfo->clause;
 	Oid			opno,
 				collation,
@@ -154,16 +163,45 @@ process_equivalence(PlannerInfo *root, RestrictInfo *restrictinfo,
 									   collation);
 
 	/*
-	 * Reject clauses of the form X=X.  These are not as redundant as they
-	 * might seem at first glance: assuming the operator is strict, this is
-	 * really an expensive way to write X IS NOT NULL.  So we must not risk
-	 * just losing the clause, which would be possible if there is already a
-	 * single-element EquivalenceClass containing X.  The case is not common
-	 * enough to be worth contorting the EC machinery for, so just reject the
-	 * clause and let it be processed as a normal restriction clause.
+	 * Clauses of the form X=X cannot be translated into EquivalenceClasses.
+	 * We'd either end up with a single-entry EC, losing the knowledge that
+	 * the clause was present at all, or else make an EC with duplicate
+	 * entries, causing other issues.
 	 */
 	if (equal(item1, item2))
-		return false;			/* X=X is not a useful equivalence */
+	{
+		/*
+		 * If the operator is strict, then the clause can be treated as just
+		 * "X IS NOT NULL".  (Since we know we are considering a top-level
+		 * qual, we can ignore the difference between FALSE and NULL results.)
+		 * It's worth making the conversion because we'll typically get a much
+		 * better selectivity estimate than we would for X=X.
+		 *
+		 * If the operator is not strict, we can't be sure what it will do
+		 * with NULLs, so don't attempt to optimize it.
+		 */
+		set_opfuncid((OpExpr *) clause);
+		if (func_strict(((OpExpr *) clause)->opfuncid))
+		{
+			NullTest   *ntest = makeNode(NullTest);
+
+			ntest->arg = item1;
+			ntest->nulltesttype = IS_NOT_NULL;
+			ntest->argisrow = false;	/* correct even if composite arg */
+			ntest->location = -1;
+
+			*p_restrictinfo =
+				make_restrictinfo((Expr *) ntest,
+								  restrictinfo->is_pushed_down,
+								  restrictinfo->outerjoin_delayed,
+								  restrictinfo->pseudoconstant,
+								  restrictinfo->security_level,
+								  NULL,
+								  restrictinfo->outer_relids,
+								  restrictinfo->nullable_relids);
+		}
+		return false;
+	}
 
 	/*
 	 * If below outer join, check for strictness, else reject.
@@ -1741,7 +1779,7 @@ reconsider_outer_join_clause(PlannerInfo *root, RestrictInfo *rinfo,
 												   bms_copy(inner_relids),
 												   bms_copy(inner_nullable_relids),
 												   cur_ec->ec_min_security);
-			if (process_equivalence(root, newrinfo, true))
+			if (process_equivalence(root, &newrinfo, true))
 				match = true;
 		}
 
@@ -1884,7 +1922,7 @@ reconsider_full_join_clause(PlannerInfo *root, RestrictInfo *rinfo)
 													   bms_copy(left_relids),
 													   bms_copy(left_nullable_relids),
 													   cur_ec->ec_min_security);
-				if (process_equivalence(root, newrinfo, true))
+				if (process_equivalence(root, &newrinfo, true))
 					matchleft = true;
 			}
 			eq_op = select_equality_operator(cur_ec,
@@ -1899,7 +1937,7 @@ reconsider_full_join_clause(PlannerInfo *root, RestrictInfo *rinfo)
 													   bms_copy(right_relids),
 													   bms_copy(right_nullable_relids),
 													   cur_ec->ec_min_security);
-				if (process_equivalence(root, newrinfo, true))
+				if (process_equivalence(root, &newrinfo, true))
 					matchright = true;
 			}
 		}
diff --git a/src/backend/optimizer/plan/initsplan.c b/src/backend/optimizer/plan/initsplan.c
index 9931dddba43..974eb58d837 100644
--- a/src/backend/optimizer/plan/initsplan.c
+++ b/src/backend/optimizer/plan/initsplan.c
@@ -1964,10 +1964,11 @@ distribute_qual_to_rels(PlannerInfo *root, Node *clause,
 		if (maybe_equivalence)
 		{
 			if (check_equivalence_delay(root, restrictinfo) &&
-				process_equivalence(root, restrictinfo, below_outer_join))
+				process_equivalence(root, &restrictinfo, below_outer_join))
 				return;
 			/* EC rejected it, so set left_ec/right_ec the hard way ... */
-			initialize_mergeclause_eclasses(root, restrictinfo);
+			if (restrictinfo->mergeopfamilies)	/* EC might have changed this */
+				initialize_mergeclause_eclasses(root, restrictinfo);
 			/* ... and fall through to distribute_restrictinfo_to_rels */
 		}
 		else if (maybe_outer_join && restrictinfo->can_join)
diff --git a/src/include/optimizer/paths.h b/src/include/optimizer/paths.h
index a15eee54bb8..ea886b6501b 100644
--- a/src/include/optimizer/paths.h
+++ b/src/include/optimizer/paths.h
@@ -127,7 +127,8 @@ typedef bool (*ec_matches_callback_type) (PlannerInfo *root,
 										  EquivalenceMember *em,
 										  void *arg);
 
-extern bool process_equivalence(PlannerInfo *root, RestrictInfo *restrictinfo,
+extern bool process_equivalence(PlannerInfo *root,
+					RestrictInfo **p_restrictinfo,
 					bool below_outer_join);
 extern Expr *canonicalize_ec_expression(Expr *expr,
 						   Oid req_type, Oid req_collation);
diff --git a/src/test/regress/expected/equivclass.out b/src/test/regress/expected/equivclass.out
index a96b2a1b07c..c448d85dec3 100644
--- a/src/test/regress/expected/equivclass.out
+++ b/src/test/regress/expected/equivclass.out
@@ -421,3 +421,21 @@ reset session authorization;
 revoke select on ec0 from regress_user_ectest;
 revoke select on ec1 from regress_user_ectest;
 drop user regress_user_ectest;
+-- check that X=X is converted to X IS NOT NULL when appropriate
+explain (costs off)
+  select * from tenk1 where unique1 = unique1 and unique2 = unique2;
+                         QUERY PLAN                          
+-------------------------------------------------------------
+ Seq Scan on tenk1
+   Filter: ((unique1 IS NOT NULL) AND (unique2 IS NOT NULL))
+(2 rows)
+
+-- this could be converted, but isn't at present
+explain (costs off)
+  select * from tenk1 where unique1 = unique1 or unique2 = unique2;
+                       QUERY PLAN                       
+--------------------------------------------------------
+ Seq Scan on tenk1
+   Filter: ((unique1 = unique1) OR (unique2 = unique2))
+(2 rows)
+
diff --git a/src/test/regress/sql/equivclass.sql b/src/test/regress/sql/equivclass.sql
index 0e4aa0cd2c5..85aa65de392 100644
--- a/src/test/regress/sql/equivclass.sql
+++ b/src/test/regress/sql/equivclass.sql
@@ -254,3 +254,11 @@ revoke select on ec0 from regress_user_ectest;
 revoke select on ec1 from regress_user_ectest;
 
 drop user regress_user_ectest;
+
+-- check that X=X is converted to X IS NOT NULL when appropriate
+explain (costs off)
+  select * from tenk1 where unique1 = unique1 and unique2 = unique2;
+
+-- this could be converted, but isn't at present
+explain (costs off)
+  select * from tenk1 where unique1 = unique1 or unique2 = unique2;