diff --git a/NEWS b/NEWS
index 83b2f4882..8967620df 100644
--- a/NEWS
+++ b/NEWS
@@ -140,6 +140,10 @@ New in spot 2.4.1.dev (not yet released)
     optimization for stutter-invariant automata that may produce slightly
     smaller automata.
 
+  - acc_cond::name(fmt) is a new method that name well-known acceptance
+    conditions.   The fmt parameter specify the format to use for that
+    name (e.g. to the style used in HOA, or that used by print_dot()).
+
   Deprecation notices:
 
   (These functions still work but compilers emit warnings.)
diff --git a/spot/twa/acc.cc b/spot/twa/acc.cc
index 4b31f9ae1..f3eb97417 100644
--- a/spot/twa/acc.cc
+++ b/spot/twa/acc.cc
@@ -1498,6 +1498,164 @@ namespace spot
   }
 
 
+  /// Return the name of this acceptance condition, in the
+  /// specified format.
+  std::string acc_cond::name(const char* fmt) const
+  {
+    bool accentuated = false;
+    bool no_extra_param = false;
+    bool no_main_param = false;
+    bool no_parity_param = false;
+    bool abbreviate = false;
+    bool like_names = false;
+    bool other = false;
+
+    if (fmt)
+      while (*fmt)
+        switch (char c = *fmt++)
+          {
+          case '0':               // no param style
+            no_extra_param = no_main_param = no_parity_param = true;
+            break;
+          case 'a':
+            accentuated = true;
+            break;
+          case 'b':
+            abbreviate = true;
+            break;
+          case 'd':               // print_dot() style
+            accentuated = no_extra_param = abbreviate = like_names = true;
+            break;
+          case 'g':
+            no_extra_param = true;
+            break;
+          case 'l':
+            like_names = true;
+            break;
+          case 'm':
+            no_main_param = true;
+            break;
+          case 'p':
+            no_parity_param = true;
+            break;
+          case 'o':
+            other = true;
+            break;
+          case 's':
+            other = no_extra_param = no_main_param = no_parity_param =
+              like_names = true;
+            break;
+          default:
+            throw std::runtime_error
+              (std::string("unknown option for acc_cond::name(): ") + c);
+          }
+
+    std::ostringstream os;
+
+    auto gen = [abbreviate]()
+      {
+        return abbreviate ? "gen. " : "generalized-";
+      };
+    auto sets = [no_main_param, this]() -> std::string
+      {
+        return no_main_param ? "" : " " + std::to_string(num_sets());
+      };
+
+    if (is_generalized_buchi())
+      {
+        if (is_all())
+          os << "all";
+        else if (is_buchi())
+          os << (accentuated ? "Büchi" : "Buchi");
+        else
+          os << gen() << (accentuated ? "Büchi" : "Buchi") << sets();
+      }
+    else if (is_generalized_co_buchi())
+      {
+        if (is_none())
+          os << "none";
+        else if (is_co_buchi())
+          os << (accentuated ? "co-Büchi" : "co-Buchi");
+        else
+          os << gen() << (accentuated ? "co-Büchi" : "co-Buchi") << sets();
+      }
+    else
+      {
+        int r = is_rabin();
+        assert(r != 0);
+        if (r > 0)
+          {
+            os << "Rabin";
+            if (!no_main_param)
+              os << ' ' << r;
+          }
+        else
+          {
+            r = is_streett();
+            assert(r != 0);
+            if (r > 0)
+              {
+                os << "Streett";
+                if (!no_main_param)
+                  os << ' ' << r;
+              }
+            else
+              {
+                std::vector<unsigned> pairs;
+                if (is_generalized_rabin(pairs))
+                  {
+                    os << gen() << "Rabin";
+                    if (!no_main_param)
+                      {
+                        os << ' ' << pairs.size();
+                        if (!no_extra_param)
+                          for (auto p: pairs)
+                            os << ' ' << p;
+                      }
+                  }
+                else
+                  {
+                    bool max = false;
+                    bool odd = false;
+                    if (is_parity(max, odd))
+                      {
+                        os << "parity";
+                        if (!no_parity_param)
+                          os << (max ? " max" : " min")
+                             << (odd ? " odd" : " even");
+                        os << sets();
+                      }
+                    else if (like_names)
+                      {
+                        std::vector<acc_cond::rs_pair> r_pairs;
+                        bool r_like = is_rabin_like(r_pairs);
+                        unsigned rsz = r_pairs.size();
+                        std::vector<acc_cond::rs_pair> s_pairs;
+                        bool s_like = is_streett_like(s_pairs);
+                        unsigned ssz = s_pairs.size();
+                        if (r_like && (!s_like || (rsz <= ssz)))
+                          {
+                            os << "Rabin-like";
+                            if (!no_main_param)
+                              os << ' ' << rsz;
+                          }
+                        else if (s_like && (!r_like || (ssz < rsz)))
+                          {
+                            os << "Streett-like";
+                            if (!no_main_param)
+                              os << ' ' << ssz;
+                          }
+                      }
+                  }
+              }
+          }
+      }
+    std::string res = os.str();
+    if (other && res.empty())
+      res = "other" + sets();
+    return res;
+  }
+
 
   namespace
   {
diff --git a/spot/twa/acc.hh b/spot/twa/acc.hh
index e17f7feae..26fb9a5e4 100644
--- a/spot/twa/acc.hh
+++ b/spot/twa/acc.hh
@@ -33,6 +33,7 @@ namespace spot
   {
     class mark_container;
   }
+
   class SPOT_API acc_cond
   {
   public:
@@ -899,7 +900,6 @@ namespace spot
                std::function<void(std::ostream&, int)>
                set_printer = nullptr) const;
 
-
       /// \brief Construct an acc_code from a string.
       ///
       /// The string can follow the following grammar:
@@ -1313,6 +1313,19 @@ namespace spot
       return {num_sets(), code_.remove(all_sets() - rem, true)};
     }
 
+    /// \brief Return the name of this acceptance condition, in the
+    /// specified format.
+    ///
+    /// The empty string is returned if no name is known.
+    ///
+    /// \a fmt should be a combination of the following letters.  (0)
+    /// no parameters, (a) accentuated, (b) abbreviated, (d) style
+    /// used in dot output, (g) no generalized parameter, (l)
+    /// recognize Street-like and Rabin-like, (m) no main parameter,
+    /// (p) no parity parameter, (o) name unknown acceptance as
+    /// 'other', (s) shorthand for 'lo0'.
+    std::string name(const char* fmt = "alo") const;
+
   protected:
     mark_t::value_t all_sets_() const
     {
diff --git a/spot/twaalgos/dot.cc b/spot/twaalgos/dot.cc
index 5e1aefee4..cb8efa123 100644
--- a/spot/twaalgos/dot.cc
+++ b/spot/twaalgos/dot.cc
@@ -455,85 +455,9 @@ namespace spot
           }
       }
 
-      std::string get_acceptance_for_human()
-      {
-        std::ostringstream os;
-
-        if (aut_->acc().is_generalized_buchi())
-          {
-            if (aut_->acc().is_all())
-              os << "all";
-            else if (aut_->acc().is_buchi())
-              os << "Büchi";
-            else
-              os << "gen. Büchi " << aut_->num_sets();
-          }
-        else if (aut_->acc().is_generalized_co_buchi())
-          {
-            if (aut_->acc().is_none())
-              os << "none";
-            else if (aut_->acc().is_co_buchi())
-              os << "co-Büchi";
-            else
-              os << "gen. co-Büchi " << aut_->num_sets();
-          }
-        else
-          {
-            int r = aut_->acc().is_rabin();
-            assert(r != 0);
-            if (r > 0)
-              {
-                os << "Rabin " << r;
-              }
-            else
-              {
-                r = aut_->acc().is_streett();
-                assert(r != 0);
-                if (r > 0)
-                  {
-                    os << "Streett " << r;
-                  }
-                else
-                  {
-                    std::vector<unsigned> pairs;
-                    if (aut_->acc().is_generalized_rabin(pairs))
-                      {
-                        os << "gen. Rabin " << pairs.size();
-                      }
-                    else
-                      {
-                        bool max = false;
-                        bool odd = false;
-                        if (aut_->acc().is_parity(max, odd))
-                          {
-                            os << "parity "
-                               << (max ? "max " : "min ")
-                               << (odd ? "odd " : "even ")
-                               << aut_->num_sets();
-                          }
-                        else
-                          {
-                            std::vector<acc_cond::rs_pair> r_pairs;
-                            bool r_like = aut_->acc().is_rabin_like(r_pairs);
-                            unsigned rsz = r_pairs.size();
-                            std::vector<acc_cond::rs_pair> s_pairs;
-                            bool s_like = aut_->acc().is_streett_like(s_pairs);
-                            unsigned ssz = s_pairs.size();
-                            if (r_like && (!s_like || (rsz <= ssz)))
-                              os << "Rabin-like " << rsz;
-                           else if (s_like && (!r_like || (ssz < rsz)))
-                              os << "Streett-like " << ssz;
-                          }
-                      }
-                  }
-              }
-          }
-        return os.str();
-      }
-
       void print_acceptance_for_human()
       {
-        std::string accstr = get_acceptance_for_human();
+        std::string accstr = aut_->acc().name("d");
         if (accstr.empty())
           return;
         os_ << nl_ << '[' << accstr << ']';
diff --git a/tests/python/acc_cond.ipynb b/tests/python/acc_cond.ipynb
index 1922bcf23..bcff265be 100644
--- a/tests/python/acc_cond.ipynb
+++ b/tests/python/acc_cond.ipynb
@@ -15,7 +15,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.4"
+   "version": "3.6.3"
   },
   "name": ""
  },
@@ -1266,6 +1266,36 @@
      ],
      "prompt_number": 46
     },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "If the acceptance condition has some known name, it can be retrieved using the `name()` method.  By default the name given is a human-readable string close that used in the HOA format, but with proper accents, and support for name like `Streett-like` or `Rabin-like`.  The argument `arg` can specify a different style using the same syntax as in `--format='%[arg]g'` when using the command-line tools."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "print(acc.name())\n",
+      "print(acc.name(\"d\"))  # <- Style used by print_dot(aut, \"a\")\n",
+      "print(acc.name(\"0\"))  # <- no parameters"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "generalized-B\u00fcchi 4\n",
+        "gen. B\u00fcchi 4\n",
+        "generalized-Buchi\n"
+       ]
+      }
+     ],
+     "prompt_number": 47
+    },
     {
      "cell_type": "markdown",
      "metadata": {},
@@ -1293,7 +1323,7 @@
        ]
       }
      ],
-     "prompt_number": 47
+     "prompt_number": 48
     },
     {
      "cell_type": "markdown",
@@ -1314,13 +1344,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 48,
+       "prompt_number": 49,
        "text": [
         "{0,1,2,3}"
        ]
       }
      ],
-     "prompt_number": 48
+     "prompt_number": 49
     },
     {
      "cell_type": "markdown",
@@ -1351,7 +1381,7 @@
        ]
       }
      ],
-     "prompt_number": 49
+     "prompt_number": 50
     },
     {
      "cell_type": "markdown",
@@ -1381,7 +1411,7 @@
        ]
       }
      ],
-     "prompt_number": 50
+     "prompt_number": 51
     },
     {
      "cell_type": "code",
@@ -1403,7 +1433,7 @@
        ]
       }
      ],
-     "prompt_number": 51
+     "prompt_number": 52
     },
     {
      "cell_type": "code",
@@ -1425,7 +1455,7 @@
        ]
       }
      ],
-     "prompt_number": 52
+     "prompt_number": 53
     }
    ],
    "metadata": {}