diff --git a/src/core/Iterator.pm6 b/src/core/Iterator.pm6
index 339b2835cbb..4b65eb4491f 100644
--- a/src/core/Iterator.pm6
+++ b/src/core/Iterator.pm6
@@ -131,4 +131,12 @@ my role PredictiveIterator does Iterator {
     method bool-only(--> Bool:D) { self.count-only.Bool }
 }
 
+# The CachedIterator role is a refinement of the PredictiveIterator role for
+# those cases when all values have been generated already.  It prevents the
+# already generated values from being cached yet again for a Sequence.
+my role CachedIterator does PredictiveIterator {
+    # The "cache" method should return a List of the already generated values.
+    method cache(--> List:D) { ... }
+}
+
 # vim: ft=perl6 expandtab sw=4
diff --git a/src/core/Rakudo/Iterator.pm6 b/src/core/Rakudo/Iterator.pm6
index 2e7e8805570..00c6baf7ed1 100644
--- a/src/core/Rakudo/Iterator.pm6
+++ b/src/core/Rakudo/Iterator.pm6
@@ -2612,7 +2612,7 @@ class Rakudo::Iterator {
     # Return an iterator for an Array that has been completely reified
     # already.  Returns a assignable container for elements don't exist
     # before the end of the reified array.
-    my class ReifiedArrayIterator does PredictiveIterator {
+    my class ReifiedArrayIterator does CachedIterator {
         has $!reified;
         has $!descriptor;
         has int $!i;
@@ -2701,6 +2701,9 @@ class Rakudo::Iterator {
                 - nqp::islt_i($!i,nqp::elems($!reified))
             )
         }
+        method cache(--> List:D) {
+            nqp::p6bindattrinvres(nqp::create(List),List,'$!reified',$!reified)
+        }
         method sink-all(--> IterationEnd) { $!i = nqp::elems($!reified) }
     }
     method ReifiedArray(\array, Mu \descriptor) {
@@ -2710,7 +2713,7 @@ class Rakudo::Iterator {
     # Return an iterator for a List that has been completely reified
     # already.  Returns an nqp::null for elements that don't exist
     # before the end of the reified list.
-    my class ReifiedListIterator does PredictiveIterator {
+    my class ReifiedListIterator does CachedIterator {
         has $!reified;
         has int $!i;
 
@@ -2791,6 +2794,9 @@ class Rakudo::Iterator {
                 - nqp::islt_i($!i,nqp::elems($!reified))
             )
         }
+        method cache(--> List:D) {
+            nqp::p6bindattrinvres(nqp::create(List),List,'$!reified',$!reified)
+        }
         method sink-all(--> IterationEnd) { $!i = nqp::elems($!reified) }
     }
     method ReifiedList(\list) {
diff --git a/src/core/Seq.pm6 b/src/core/Seq.pm6
index f95e231c8b5..dbbb0e04149 100644
--- a/src/core/Seq.pm6
+++ b/src/core/Seq.pm6
@@ -19,7 +19,13 @@ my class Seq is Cool does Iterable does Sequence {
         nqp::if(
           nqp::isconcrete(my \iter = $!iter),
           nqp::stmts(
-            ($!iter := Iterator),
+            ($!iter := Iterator),                 # allow usage only once
+            nqp::if(
+              nqp::istype(iter,CachedIterator),
+              nqp::bindattr(                      # can set up cache now
+                self,::?CLASS,'$!list',nqp::decont(iter.cache)
+              )
+            ),
             iter
           ),
           nqp::if(