diff --git a/src/core/Any-str.pm b/src/core/Any-str.pm
index a9406f87b24..fe88534f711 100644
--- a/src/core/Any-str.pm
+++ b/src/core/Any-str.pm
@@ -1,4 +1,8 @@
 augment class Any {
+    method ACCEPTS($topic) {
+        self === $topic
+    }
+
     our Int multi method bytes() is export {
         pir::box__PI(pir::bytelength__IS(self))
     }
diff --git a/src/core/EnumMap.pm b/src/core/EnumMap.pm
index 7b7ffb28851..30c6bf8b599 100644
--- a/src/core/EnumMap.pm
+++ b/src/core/EnumMap.pm
@@ -21,7 +21,12 @@ class EnumMap does Associative {
     }
 
     multi method ACCEPTS(Regex $topic) {
-        any(@.keys) ~~ $topic;
+        for @.keys -> $k {
+            if $topic.ACCEPTS($k) {
+                return True;
+            }
+        }
+        False
     }
 
     multi method ACCEPTS(%topic) {
diff --git a/src/core/Parcel.pm b/src/core/Parcel.pm
index 1a755a526d4..803883ff348 100644
--- a/src/core/Parcel.pm
+++ b/src/core/Parcel.pm
@@ -8,7 +8,7 @@ augment class Parcel {
         if self.elems == 0 {
             $x.notdef || ($x.does(::Positional) && $x == 0)
         } else {
-            die "Don't know how to smart-match against a Parcel that doesn't happen to be empty";
+            self.Seq.ACCEPTS($x)
         }
     }
 }
diff --git a/src/core/Seq.pm b/src/core/Seq.pm
index ac39d164706..e7eb226f594 100644
--- a/src/core/Seq.pm
+++ b/src/core/Seq.pm
@@ -1,4 +1,49 @@
 augment class Seq {
+    multi method ACCEPTS(@topic) {
+        my $self_it = self.iterator();
+        my $topic_it = @topic.iterator();
+        loop {
+            my $cur_self_elem = $self_it.get;
+            if $cur_self_elem ~~ EMPTY { last }
+            if $cur_self_elem ~~ Whatever {
+                # If we just have * left, we're done. Otherwise, we have a
+                # "target" to look for.
+                loop {
+                    $cur_self_elem = $self_it.get;
+                    if $cur_self_elem ~~ EMPTY { return True }
+                    unless $cur_self_elem ~~ Whatever {
+                        last;
+                    }
+                }
+
+                # Need to find our target in the topic, if possible.
+                loop {
+                    my $cur_topic_elem = $topic_it.get;
+                    if $cur_topic_elem ~~ EMPTY {
+                        # Ran out before finding what we wanted.
+                        return False;
+                    }
+                    elsif $cur_topic_elem === $cur_self_elem {
+                        last;
+                    }
+                }
+            }
+            else {
+                my $cur_topic_elem = $topic_it.get;
+                if $cur_topic_elem ~~ EMPTY || $cur_topic_elem !=== $cur_self_elem {
+                    return False;
+                }
+            }
+        }
+
+        # If we've nothing left to match, we're successful.
+        $topic_it.get ~~ EMPTY
+    }
+
+    multi method ACCEPTS($topic) {
+        self.ACCEPTS(@($topic))
+    }
+
     method elems() { pir::set__IP(self!fill); }
 
     method Str() {