diff --git a/NEWS b/NEWS
index 42ad55dbc..113ec0fc4 100644
--- a/NEWS
+++ b/NEWS
@@ -23,6 +23,8 @@ New in spot 2.3.1.dev (not yet released)
     to state-based acceptance could cause a superfluous initial state
     to be output in some cases (the result was still correct).
 
+  - 'ltl2tgba --any -C -M ...' would not complete automata.
+
   Deprecation notices:
 
   - Using --format=%a to print the number of atomic propositions in
diff --git a/doc/org/ltl2tgba.org b/doc/org/ltl2tgba.org
index 8381adc3f..118809f3d 100644
--- a/doc/org/ltl2tgba.org
+++ b/doc/org/ltl2tgba.org
@@ -921,32 +921,6 @@ $txt
 ltl2tgba -MD '(Xa & Fb) | Gc' -d
 #+END_SRC
 
-#+RESULTS: monitor2
-#+begin_example
-digraph G {
-  rankdir=LR
-  node [shape="circle"]
-  fontname="Lato"
-  node [fontname="Lato"]
-  edge [fontname="Lato"]
-  node[style=filled, fillcolor="#ffffa0"] edge[arrowhead=vee, arrowsize=.7]
-  I [label="", style=invis, width=0]
-  I -> 3
-  0 [label=<0>]
-  0 -> 0 [label=<1>]
-  1 [label=<1>]
-  1 -> 0 [label=<a>]
-  2 [label=<2>]
-  2 -> 2 [label=<c>]
-  3 [label=<3>]
-  3 -> 1 [label=<!c>]
-  3 -> 4 [label=<c>]
-  4 [label=<4>]
-  4 -> 0 [label=<a>]
-  4 -> 2 [label=<!a &amp; c>]
-}
-#+end_example
-
 #+BEGIN_SRC dot :file monitor2.png :cmdline -Tpng :var txt=monitor2 :exports results
 $txt
 #+END_SRC
@@ -959,6 +933,29 @@ match the formula, monitor cannot be used to check for eventualities
 such as =F(a)=: indeed, any finite execution can be extended to match
 =F(a)=.
 
+
+Because Monitors accept every recognized run (in other words, they
+only reject words that are not recognized), it makes little sense to
+use option =-C= to request /complete/ monitors.  If uou combine =-C=
+with =-M=, the result will output as a Büchi automaton if (and only
+if) a sink state had to be added.  For instance, here is the
+"complete" version of the previous monitor.
+
+#+NAME: monitor3
+#+BEGIN_SRC sh :results verbatim :exports code
+ltl2tgba -C -M -D '(Xa & Fb) | Gc' -d
+#+END_SRC
+
+#+BEGIN_SRC dot :file monitor3.png :cmdline -Tpng :var txt=monitor3 :exports results
+$txt
+#+END_SRC
+
+#+RESULTS:
+[[file:monitor3.png]]
+
+
+
+
 #  LocalWords:  ltl tgba num toc PSL Büchi automata SRC GFb invis Acc
 #  LocalWords:  ltlfilt filenames GraphViz vectorial pdf Tpdf dotex
 #  LocalWords:  sed png cmdline Tpng txt iff GFa ba utf UTF lbtt Fb
diff --git a/spot/twaalgos/postproc.cc b/spot/twaalgos/postproc.cc
index 2191b8924..5b3f2ca29 100644
--- a/spot/twaalgos/postproc.cc
+++ b/spot/twaalgos/postproc.cc
@@ -227,20 +227,21 @@ namespace spot
         else
           strip_acceptance_here(a);
 
-        if (PREF_ == Any)
-          return a;
-
-        a = do_simul(a, simul_);
-
-        // For Small,High we return the smallest between the output of
-        // the simulation, and that of the deterministic minimization.
-        if (PREF_ == Small && level_ == High && simul_)
+        if (PREF_ != Any)
           {
-            auto m = minimize_monitor(a);
-            if (m->num_states() < a->num_states())
-              a = m;
+            if (PREF_ != Deterministic)
+              a = do_simul(a, simul_);
+
+            // For Small,High we return the smallest between the output of
+            // the simulation, and that of the deterministic minimization.
+            if (PREF_ == Small && level_ == High && simul_)
+              {
+                auto m = minimize_monitor(a);
+                if (m->num_states() < a->num_states())
+                  a = m;
+              }
+            a->remove_unused_ap();
           }
-        a->remove_unused_ap();
         if (COMP_)
           a = complete(a);
         return a;
diff --git a/tests/core/monitor.test b/tests/core/monitor.test
index 504721c28..d21fb3c9d 100755
--- a/tests/core/monitor.test
+++ b/tests/core/monitor.test
@@ -1,7 +1,7 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2014, 2015, 2016 Laboratoire de Recherche et
-# Développement de l'Epita (LRDE).
+# Copyright (C) 2014-2017 Laboratoire de Recherche et Développement de
+# l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
 #
@@ -44,7 +44,7 @@ digraph G {
 }
 EOF
 
-expect ltl2tgba --monitor a --hoa<<EOF
+expect ltl2tgba --monitor a GFa --hoa<<EOF
 HOA: v1
 name: "a"
 States: 2
@@ -60,9 +60,6 @@ State: 0
 State: 1
 [0] 0
 --END--
-EOF
-
-expect ltl2tgba --monitor GFa --hoa<<EOF
 HOA: v1
 name: "GFa"
 States: 1
@@ -77,3 +74,23 @@ State: 0
 [t] 0
 --END--
 EOF
+
+# Completing a monitor can produce a Büchi automaton.
+expect ltl2tgba --any -C -M Ga <<EOF
+HOA: v1
+name: "Ga"
+States: 2
+Start: 0
+AP: 1 "a"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels state-acc complete
+properties: deterministic stutter-invariant inherently-weak
+--BODY--
+State: 0 {0}
+[0] 0
+[!0] 1
+State: 1
+[t] 1
+--END--
+EOF