diff --git a/lib/ParaSeq.rakumod b/lib/ParaSeq.rakumod
index c4075de..88e2cc4 100644
--- a/lib/ParaSeq.rakumod
+++ b/lib/ParaSeq.rakumod
@@ -63,10 +63,12 @@ my class ParaIterator does Iterator {
     has atomicint $!stop;       # stop all processing if 1
 
     method new(\parent, \pressure) {
+        # Initial buffer being empty, force fetching first batch immediately
+        my constant $empty = nqp::create(IterationBuffer);
+
         my $self := nqp::create(self);
         nqp::bindattr($self,ParaIterator,'$!parent',parent);
-        nqp::push((my $current := nqp::create(IterationBuffer)),Mu);
-        nqp::bindattr($self,ParaIterator,'$!current',$current);
+        nqp::bindattr($self,ParaIterator,'$!current',$empty);
         nqp::bindattr($self,ParaIterator,'$!queues',nqp::create(ParaQueue));
         nqp::bindattr($self,ParaIterator,'$!pressure',pressure);
         $self
@@ -90,22 +92,26 @@ my class ParaIterator does Iterator {
 
     method !next-batch(\next) {
         nqp::push($!pressure,Mu);  # initiate more work
+
         $!delivered = nqp::add_i(
           $!delivered,
-          nqp::sub_i(nqp::elems($!current := nqp::shift(next)),1)
+          nqp::elems(my $buffer := nqp::shift(next))
         );
-        $!current
+        $buffer
     }
 
     method pull-one() {
-        my $pulled := nqp::shift($!current);
 
-        nqp::until(
+        nqp::if(
           nqp::elems($!current),
+          (my $pulled := nqp::shift($!current)),
           nqp::if(
             nqp::eqaddr((my $next := nqp::shift($!queues)),IterationEnd),
             (return IterationEnd),
-            ($pulled := nqp::shift(self!next-batch($next)))
+            nqp::stmts(
+              ($!current := self!next-batch($next)),
+              ($pulled   := self.pull-one)
+            )
           )
         );
 
@@ -121,7 +127,7 @@ my class ParaIterator does Iterator {
         nqp::until(
           nqp::atomicload_i($!stop),
           nqp::stmts(
-            (my uint $elems = nqp::elems($current) - 1),
+            (my uint $elems = nqp::elems($current)),
             nqp::if(
               $elems > $toskip,  # can't ignore whole buffer, only part
               nqp::stmts(
@@ -134,7 +140,7 @@ my class ParaIterator does Iterator {
               (return 0)         # really done
             ),
             ($toskip = nqp::sub_i($toskip,$elems)),
-            ($current := self!next-batch($next))
+            ($current := $!current := self!next-batch($next))
           )
         );
 
@@ -149,13 +155,12 @@ my class ParaIterator does Iterator {
         nqp::until(
           nqp::atomicload_i($!stop),
           nqp::stmts(
-            (my $stats := nqp::pop($current)),
             target.append($current),
             nqp::if(
               nqp::eqaddr((my $next := nqp::shift($queues)),IterationEnd),
               (return IterationEnd),
               ($current := self!next-batch($next))
-            ),
+            )
           )
         );
 
@@ -518,7 +523,7 @@ class ParaSeq {
         nqp::atomicadd_i($!processed,$processed);
         nqp::atomicadd_i($!produced, $produced );
         nqp::atomicadd_i($!nsecs,    $nsecs    );
-        ParaStats.new($ordinal, $processed, $produced, $nsecs)
+#        ParaStats.new($ordinal, $processed, $produced, $nsecs)
     }
 
     # Mark the given queue as done
@@ -529,14 +534,14 @@ class ParaSeq {
         # If we're still running
         unless nqp::atomicload_i($!stop) {
             # Push the statistics as the last element in the output
-            nqp::push(
-              nqp::decont($output),
+#            nqp::push(
+#              nqp::decont($output),
               self!add-stats(
                 $ordinal,
                 nqp::elems(nqp::decont($input)),
                 nqp::elems(nqp::decont($output)),
                 nqp::time() - $then
-              )
+#              )
             );
 
             # Make the produced values available to the result iterator