diff --git a/src/compiler/scala/tools/nsc/transform/patmat/MatchAnalysis.scala b/src/compiler/scala/tools/nsc/transform/patmat/MatchAnalysis.scala
index 94f3ea37171b..8f37cde0ed71 100644
--- a/src/compiler/scala/tools/nsc/transform/patmat/MatchAnalysis.scala
+++ b/src/compiler/scala/tools/nsc/transform/patmat/MatchAnalysis.scala
@@ -541,6 +541,7 @@ trait MatchAnalysis extends MatchApproximation {
         approx.fullRewrite.applyOrElse[TreeMaker, Prop](tm, {
           case BodyTreeMaker(_, _) => True // irrelevant -- will be discarded by symbolCase later
           case ExtractorTreeMaker(_, _, _)
+             | ProductExtractorTreeMaker(_, _)
              | GuardTreeMaker(_) =>
             if (strict) False else True
           case _ => // debug.patmat("backing off due to "+ tm)
diff --git a/test/files/neg/t5365e.check b/test/files/neg/t5365e.check
new file mode 100644
index 000000000000..77f4e59e2fa8
--- /dev/null
+++ b/test/files/neg/t5365e.check
@@ -0,0 +1,23 @@
+t5365e.scala:7: warning: match may not be exhaustive.
+It would fail on the following input: Bar(_)
+  def f0(x: Exh) = x match { case Foo()        => ()                         } // don't back off
+                   ^
+t5365e.scala:8: warning: match may not be exhaustive.
+It would fail on the following input: Bar(_)
+  def f1(x: Exh) = x match { case Foo(x)       => x                          } // don't back off
+                   ^
+t5365e.scala:9: warning: match may not be exhaustive.
+It would fail on the following input: Bar(_)
+  def f2(x: Exh) = x match { case Foo(x, y)    => x + y                      } // don't back off
+                   ^
+t5365e.scala:10: warning: match may not be exhaustive.
+It would fail on the following input: Bar(_)
+  def fX(x: Exh) = x match { case Foo(xs @ _*) => xs                         } // don't back off
+                   ^
+t5365e.scala:11: warning: match may not be exhaustive.
+It would fail on the following input: Foo(_)
+  def b1(x: Exh) = x match {                                case Bar(x) => x } // inexhaustive
+                   ^
+error: No warnings can be incurred under -Xfatal-warnings.
+5 warnings found
+one error found
diff --git a/test/files/neg/t5365e.flags b/test/files/neg/t5365e.flags
new file mode 100644
index 000000000000..85d8eb2ba295
--- /dev/null
+++ b/test/files/neg/t5365e.flags
@@ -0,0 +1 @@
+-Xfatal-warnings
diff --git a/test/files/neg/t5365e.scala b/test/files/neg/t5365e.scala
new file mode 100644
index 000000000000..fb77bd97bae3
--- /dev/null
+++ b/test/files/neg/t5365e.scala
@@ -0,0 +1,19 @@
+sealed trait Exh
+final case class Foo(xs: String*) extends Exh
+final case class Bar(x: String)   extends Exh
+
+class Main {
+  def ex(x: Exh) = x match { case Foo(xs @ _*) => xs        case Bar(x) => x } // exhaustive
+  def f0(x: Exh) = x match { case Foo()        => ()                         } // don't back off
+  def f1(x: Exh) = x match { case Foo(x)       => x                          } // don't back off
+  def f2(x: Exh) = x match { case Foo(x, y)    => x + y                      } // don't back off
+  def fX(x: Exh) = x match { case Foo(xs @ _*) => xs                         } // don't back off
+  def b1(x: Exh) = x match {                                case Bar(x) => x } // inexhaustive
+  def fb(x: Exh) = x match { case Foo(x)       => x         case Bar(x) => x } // optimistically exhaustive
+  // ^ under -Xstrict-patmat-analysis pessimistically approximates case Foo(x) as inexhaustive:
+  //     test/files/neg/t5365e.scala:12: warning: match may not be exhaustive.
+  //     It would fail on the following input: Foo(_)
+  //       def fb(x: Exh) = x match { case Foo(x)       => x         case Bar(x) => x } // optimistically exhaustive
+  //                        ^
+  // ... and the counter-example needs work -.- ...
+}
diff --git a/test/files/run/virtpatmat_unapplyprod.check b/test/files/run/virtpatmat_unapplyprod.check
index 2660ff8f96a2..87f3008a967a 100644
--- a/test/files/run/virtpatmat_unapplyprod.check
+++ b/test/files/run/virtpatmat_unapplyprod.check
@@ -1,3 +1,7 @@
+virtpatmat_unapplyprod.scala:19: warning: match may not be exhaustive.
+It would fail on the following inputs: FooSeq((x: Int forSome x not in 1), "a", _), FooSeq((x: Int forSome x not in 1), (x: String forSome x not in "a"), _), FooSeq(1, (x: String forSome x not in "a"), _)
+  FooSeq(1, "a", true, false, true) match {
+        ^
 (2,3)
 (2,3)
 (2,3)