diff --git a/compiler/src/dotty/tools/dotc/transform/patmat/Space.scala b/compiler/src/dotty/tools/dotc/transform/patmat/Space.scala
index bce2752d7164..05b3ea66bc30 100644
--- a/compiler/src/dotty/tools/dotc/transform/patmat/Space.scala
+++ b/compiler/src/dotty/tools/dotc/transform/patmat/Space.scala
@@ -708,6 +708,38 @@ class SpaceEngine(implicit ctx: Context) extends SpaceLogic {
     else text
   }
 
+  /** Whether the counterexample is satisfiable. The space is flattened and non-empty. */
+  def satisfiable(sp: Space): Boolean = {
+    def impossible: Nothing = throw new AssertionError("`satisfiable` only accepts flattened space.")
+
+    def genConstraint(space: Space): List[(Type, Type)] = space match {
+      case Prod(tp, unappTp, unappSym, ss, _) =>
+        val tps = signature(unappTp, unappSym, ss.length)
+        ss.zip(tps).flatMap {
+          case (sp : Prod, tp) => sp.tp -> tp :: genConstraint(sp)
+          case (Typ(tp1, _), tp2) => tp1 -> tp2 :: Nil
+          case _ => impossible
+        }
+      case Typ(_, _) => Nil
+      case _ => impossible
+    }
+
+    def checkConstraint(constrs: List[(Type, Type)])(implicit ctx: Context): Boolean = {
+      val tvarMap = collection.mutable.Map.empty[Symbol, TypeVar]
+      val typeParamMap = new TypeMap() {
+        override def apply(tp: Type): Type = tp match {
+          case tref: TypeRef if tref.symbol.is(TypeParam) =>
+            tvarMap.getOrElseUpdate(tref.symbol, newTypeVar(tref.underlying.bounds))
+          case tp => mapOver(tp)
+        }
+      }
+
+      constrs.forall { case (tp1, tp2) => typeParamMap(tp1) <:< typeParamMap(tp2) }
+    }
+
+    checkConstraint(genConstraint(sp))(ctx.fresh.setNewTyperState())
+  }
+
   /** Display spaces */
   def show(s: Space): String = {
     def params(tp: Type): List[Type] = tp.classSymbol.primaryConstructor.info.firstParamTypes
@@ -775,6 +807,16 @@ class SpaceEngine(implicit ctx: Context) extends SpaceLogic {
     res
   }
 
+  /** Whehter counter-examples should be further checked? True for GADTs. */
+  def shouldCheckExamples(tp: Type): Boolean = {
+    new TypeAccumulator[Boolean] {
+      override def apply(b: Boolean, tp: Type): Boolean = tp match {
+        case tref: TypeRef if tref.symbol.is(TypeParam) && variance != 1 => true
+        case tp => b || foldOver(b, tp)
+      }
+    }.apply(false, tp)
+  }
+
   def checkExhaustivity(_match: Match): Unit = {
     val Match(sel, cases) = _match
     val selTyp = sel.tpe.widen.dealias
@@ -785,10 +827,15 @@ class SpaceEngine(implicit ctx: Context) extends SpaceLogic {
       debug.println(s"${x.pat.show} ====> ${show(space)}")
       space
     }).reduce((a, b) => Or(List(a, b)))
-    val uncovered = simplify(minus(Typ(selTyp, true), patternSpace), aggressive = true)
 
-    if (uncovered != Empty)
-      ctx.warning(PatternMatchExhaustivity(show(uncovered)), sel.pos)
+    val checkGADTSAT = shouldCheckExamples(selTyp)
+
+    val uncovered =
+      flatten(simplify(minus(Typ(selTyp, true), patternSpace), aggressive = true))
+        .filter(s => s != Empty && (!checkGADTSAT || satisfiable(s)))
+
+    if (uncovered.nonEmpty)
+      ctx.warning(PatternMatchExhaustivity(show(Or(uncovered))), sel.pos)
   }
 
   def checkRedundancy(_match: Match): Unit = {
diff --git a/tests/patmat/3454.scala b/tests/patmat/3454.scala
new file mode 100644
index 000000000000..db84e8b2c921
--- /dev/null
+++ b/tests/patmat/3454.scala
@@ -0,0 +1,10 @@
+object O {
+  sealed trait Expr[T]
+  case class BExpr(bool: Boolean) extends Expr[Boolean]
+  case class IExpr(int: Int) extends Expr[Int]
+
+  def join[T](e1: Expr[T], e2: Expr[T]): Expr[T] = (e1, e2) match {
+    case (IExpr(i1), IExpr(i2)) => IExpr(i1 + i2)
+    case (BExpr(b1), BExpr(b2)) => BExpr(b1 & b2)
+  }
+}
\ No newline at end of file
diff --git a/tests/patmat/exhausting.check b/tests/patmat/exhausting.check
index d17c5f36bc80..86ec004acac6 100644
--- a/tests/patmat/exhausting.check
+++ b/tests/patmat/exhausting.check
@@ -3,4 +3,4 @@
 32: Pattern Match Exhaustivity: List(_, _: _*)
 39: Pattern Match Exhaustivity: Bar3
 44: Pattern Match Exhaustivity: (Bar2, Bar2)
-53: Pattern Match Exhaustivity: (Bar2, Bar2), (Bar2, Bar1), (Bar1, Bar3), (Bar1, Bar2)
+50: Pattern Match Exhaustivity: (Bar2, Bar2)
diff --git a/tests/patmat/exhausting.scala b/tests/patmat/exhausting.scala
index 75daf4b9112a..640c9e88b100 100644
--- a/tests/patmat/exhausting.scala
+++ b/tests/patmat/exhausting.scala
@@ -46,9 +46,6 @@ object Test {
     case (Bar2, Bar3) => ()
     case (Bar3, _) => ()
   }
-  // fails for: (Bar1, Bar2)
-  // fails for: (Bar1, Bar3)
-  // fails for: (Bar2, Bar1)
   // fails for: (Bar2, Bar2)
   def fail5[T](xx: (Foo[T], Foo[T])) = xx match {
     case (Bar1, Bar1) => ()
diff --git a/tests/patmat/gadt-basic.scala b/tests/patmat/gadt-basic.scala
new file mode 100644
index 000000000000..228b713f75bc
--- /dev/null
+++ b/tests/patmat/gadt-basic.scala
@@ -0,0 +1,23 @@
+object O1 {
+  sealed trait Expr[T]
+  case class BExpr(bool: Boolean) extends Expr[Boolean]
+  case class IExpr(int: Int) extends Expr[Int]
+
+  def join[T](e1: Expr[T], e2: Expr[T]): Expr[T] = (e1, e2) match {
+    case (IExpr(i1), IExpr(i2)) => IExpr(i1 + i2)
+    case (BExpr(b1), BExpr(b2)) => BExpr(b1 & b2)
+  }
+}
+
+object O2 {
+  sealed trait GADT[A, B]
+  case object IntString extends GADT[Int, String]
+  case object IntFloat extends GADT[Int, Float]
+  case object FloatFloat extends GADT[Float, Float]
+
+  def m[A, B](g1: GADT[A, B], g2: GADT[A, B]) = (g1, g2) match {
+    case (IntString, IntString) => ;
+    case (IntFloat, IntFloat) => ;
+    case (FloatFloat, FloatFloat) => ;
+  }
+}
diff --git a/tests/patmat/gadt-covariant.check b/tests/patmat/gadt-covariant.check
new file mode 100644
index 000000000000..4d8fd60c890b
--- /dev/null
+++ b/tests/patmat/gadt-covariant.check
@@ -0,0 +1 @@
+6: Pattern Match Exhaustivity: (BExpr(_), IExpr(_)), (IExpr(_), BExpr(_))
diff --git a/tests/patmat/gadt-covariant.scala b/tests/patmat/gadt-covariant.scala
new file mode 100644
index 000000000000..aadcda9a3efb
--- /dev/null
+++ b/tests/patmat/gadt-covariant.scala
@@ -0,0 +1,10 @@
+object O {
+   sealed trait Expr[+T]
+   case class IExpr(x: Int) extends Expr[Int]
+   case class BExpr(b: Boolean) extends Expr[Boolean]
+
+   def foo[T](x: Expr[T], y: Expr[T]) = (x, y) match {
+      case (IExpr(_), IExpr(_)) => true
+      case (BExpr(_), BExpr(_)) => false
+   }
+}
\ No newline at end of file
diff --git a/tests/patmat/gadt-invariant.scala b/tests/patmat/gadt-invariant.scala
new file mode 100644
index 000000000000..c72ea949f373
--- /dev/null
+++ b/tests/patmat/gadt-invariant.scala
@@ -0,0 +1,10 @@
+object O {
+   sealed trait Expr[T]
+   case class IExpr(x: Int) extends Expr[Int]
+   case class BExpr(b: Boolean) extends Expr[Boolean]
+
+   def foo[T](x: Expr[T], y: Expr[T]) = (x, y) match {
+      case (IExpr(_), IExpr(_)) => true
+      case (BExpr(_), BExpr(_)) => false
+   }
+}
\ No newline at end of file
diff --git a/tests/patmat/gadt-nontrivial.check b/tests/patmat/gadt-nontrivial.check
new file mode 100644
index 000000000000..c005f8d1c0cc
--- /dev/null
+++ b/tests/patmat/gadt-nontrivial.check
@@ -0,0 +1 @@
+7: Pattern Match Exhaustivity: (IntExpr(_), AddExpr(_, _))
diff --git a/tests/patmat/gadt-nontrivial.scala b/tests/patmat/gadt-nontrivial.scala
new file mode 100644
index 000000000000..a9ab5f3da7a2
--- /dev/null
+++ b/tests/patmat/gadt-nontrivial.scala
@@ -0,0 +1,12 @@
+object O {
+  sealed trait Expr[T]
+  case class BoolExpr(v: Boolean) extends Expr[Boolean]
+  case class IntExpr(v: Int) extends Expr[Int]
+  case class AddExpr(e1: Expr[Int], e2: Expr[Int]) extends Expr[Int]
+
+  def join[T](e1: Expr[T], e2: Expr[T]): Expr[T] = (e1, e2) match {
+    case (BoolExpr(b1), BoolExpr(b2)) => BoolExpr(b1 && b2)
+    case (IntExpr(i1), IntExpr(i2)) => IntExpr(i1 + i2)
+    case (AddExpr(ei1, ei2), ie) => join(join(ei1, ei2), ie)
+  }
+}
diff --git a/tests/patmat/gadt-nontrivial2.check b/tests/patmat/gadt-nontrivial2.check
new file mode 100644
index 000000000000..3446c79d6706
--- /dev/null
+++ b/tests/patmat/gadt-nontrivial2.check
@@ -0,0 +1 @@
+13:
\ No newline at end of file
diff --git a/tests/patmat/gadt-nontrivial2.scala b/tests/patmat/gadt-nontrivial2.scala
new file mode 100644
index 000000000000..d6fd595f004d
--- /dev/null
+++ b/tests/patmat/gadt-nontrivial2.scala
@@ -0,0 +1,16 @@
+object O {
+  sealed trait Nat
+  type Zero = Nat
+  sealed trait Succ[N <: Nat] extends Nat
+
+  sealed trait NVec[N <: Nat, +A]
+  case object NEmpty extends NVec[Zero, Nothing]
+  case class NCons[N <: Nat, +A](head: A, tail: NVec[N, A]) extends NVec[Succ[N], A]
+
+  def nzip[N <: Nat, A, B](v1: NVec[N, A], v2: NVec[N, B]): NVec[N, (A, B)] =
+    (v1, v2) match {
+      case (NEmpty, NEmpty) => NEmpty
+      case (NCons(a, atail), NCons(b, btail)) =>
+        NCons((a, b), nzip(atail, btail))
+    }
+}
diff --git a/tests/patmat/gadt3.scala.ignore b/tests/patmat/gadt3.scala
similarity index 100%
rename from tests/patmat/gadt3.scala.ignore
rename to tests/patmat/gadt3.scala
diff --git a/tests/patmat/t9926.scala b/tests/patmat/t9926.scala
new file mode 100644
index 000000000000..0f9e18a3878b
--- /dev/null
+++ b/tests/patmat/t9926.scala
@@ -0,0 +1,23 @@
+object Model {
+  sealed trait Field[T]
+  case object StringField extends Field[String]
+  case object BoolField extends Field[Boolean]
+
+  sealed trait Value[T]
+  case class Literal(v: String) extends Value[String]
+  case class Bool(v: Boolean) extends Value[Boolean]
+
+  sealed trait Expression[T]
+  case class Equality[T](field: Field[T], value: Value[T]) extends Expression[T]
+
+  def interpret[T](expr: Expression[T]): Int = expr match {
+    case Equality(StringField, Literal(v)) => 1
+    case Equality(BoolField, Bool(v)) => 2
+  }
+
+  // T - T(s1, s2, ...)
+  // if T contains type parameter, get its dimension types.
+  //
+  // actively decompose its dimensions, and then do subtype checking to
+  // see if the type paramter can be instantiated.
+}
\ No newline at end of file