diff --git a/bin/autcross.cc b/bin/autcross.cc
index 0d1ab9de7..137966342 100644
--- a/bin/autcross.cc
+++ b/bin/autcross.cc
@@ -509,8 +509,7 @@ namespace
                    const spot::const_twa_graph_ptr& aut_j,
                    size_t i, size_t j)
   {
-    if (aut_i->num_sets() + aut_j->num_sets()
-        > 8 * sizeof(spot::acc_cond::mark_t::value_t))
+    if (aut_i->num_sets() + aut_j->num_sets() > SPOT_NB_ACC)
       {
         std::cerr << "info: building " << autname(i)
                   << '*' << autname(j, true)
diff --git a/bin/autfilt.cc b/bin/autfilt.cc
index 9b0fe7419..e51450cbb 100644
--- a/bin/autfilt.cc
+++ b/bin/autfilt.cc
@@ -930,8 +930,7 @@ parse_opt(int key, char* arg, struct argp_state*)
             if (res < 0)
               error(2, 0, "acceptance sets should be non-negative:"
                     " --mask-acc=%ld", res);
-            if (static_cast<unsigned long>(res)
-                > sizeof(spot::acc_cond::mark_t::value_t))
+            if (static_cast<unsigned long>(res) > SPOT_NB_ACC)
               error(2, 0, "this implementation does not support that many"
                     " acceptance sets: --mask-acc=%ld", res);
             opt_mask_acc.set(res);
diff --git a/bin/ltlcross.cc b/bin/ltlcross.cc
index e7195bb75..4706d2f6b 100644
--- a/bin/ltlcross.cc
+++ b/bin/ltlcross.cc
@@ -691,8 +691,7 @@ namespace
                    const spot::const_twa_graph_ptr& aut_j,
                    size_t i, size_t j, bool icomp, bool jcomp)
   {
-    if (aut_i->num_sets() + aut_j->num_sets()
-        > 8 * sizeof(spot::acc_cond::mark_t::value_t))
+    if (aut_i->num_sets() + aut_j->num_sets() > SPOT_NB_ACC)
       {
         // Report the skipped test if both automata are not
         // complemented, or the --verbose option is used,
diff --git a/spot/parseaut/parseaut.yy b/spot/parseaut/parseaut.yy
index be7df7ff6..a4a0db623 100644
--- a/spot/parseaut/parseaut.yy
+++ b/spot/parseaut/parseaut.yy
@@ -772,7 +772,7 @@ header-item: "States:" INT
 			  "acceptance condition...");
 		    error(res.accset_loc, "... previously defined here.");
 		  }
-		else if ($2 > 8 * sizeof(spot::acc_cond::mark_t::value_t))
+		else if ($2 > SPOT_NB_ACC)
 		  {
 		    error(@1 + @2,
 			  "this implementation cannot support such a large "
diff --git a/spot/twa/acc.hh b/spot/twa/acc.hh
index 1cac6c534..93e6a16f2 100644
--- a/spot/twa/acc.hh
+++ b/spot/twa/acc.hh
@@ -33,19 +33,28 @@ namespace spot
   namespace internal
   {
     class mark_container;
+
+    template<bool>
+    struct _32acc {};
+    template<>
+    struct _32acc<true>
+    {
+      SPOT_DEPRECATED("mark_t no longer relies on unsigned, stop using value_t")
+      typedef unsigned value_t;
+    };
   }
 
   class SPOT_API acc_cond
   {
   public:
-    struct mark_t
+    struct mark_t : public internal::_32acc<SPOT_NB_ACC == 8*sizeof(unsigned)>
     {
-      // configure guarantees that SPOT_NB_ACC % (8*sizeof(unsigned)) == 0
-      typedef bitset<SPOT_NB_ACC / (8*sizeof(unsigned))> value_t;
-      value_t id;
-
     private:
-      mark_t(value_t id) noexcept
+      // configure guarantees that SPOT_NB_ACC % (8*sizeof(unsigned)) == 0
+      typedef bitset<SPOT_NB_ACC / (8*sizeof(unsigned))> _value_t;
+      _value_t id;
+
+      mark_t(_value_t id) noexcept
         : id(id)
       {
       }
@@ -55,7 +64,7 @@ namespace spot
 
       template<class iterator>
       mark_t(const iterator& begin, const iterator& end) noexcept
-        : mark_t(value_t::zero())
+        : mark_t(_value_t::zero())
       {
         for (iterator i = begin; i != end; ++i)
           set(*i);
@@ -86,6 +95,12 @@ namespace spot
         return res;
       }
 
+      size_t hash() const noexcept
+      {
+        std::hash<decltype(id)> h;
+        return h(id);
+      }
+
       bool operator==(unsigned o) const
       {
         SPOT_ASSERT(o == 0U);
@@ -140,12 +155,12 @@ namespace spot
 
       void set(unsigned u)
       {
-        id |= (value_t::one() << u);
+        id |= (_value_t::one() << u);
       }
 
       void clear(unsigned u)
       {
-        id &= ~(value_t::one() << u);
+        id &= ~(_value_t::one() << u);
       }
 
       mark_t& operator&=(mark_t r)
@@ -532,7 +547,7 @@ namespace spot
         if (n == 0)
           return inf({});
         acc_cond::mark_t m = mark_t::all();
-        m >>= (8*sizeof(mark_t::value_t) - n);
+        m >>= (SPOT_NB_ACC - n);
         return inf(m);
       }
 
@@ -541,7 +556,7 @@ namespace spot
         if (n == 0)
           return fin({});
         acc_cond::mark_t m = mark_t::all();
-        m >>= (8*sizeof(mark_t::value_t) - n);
+        m >>= (SPOT_NB_ACC - n);
         return fin(m);
       }
 
@@ -1202,7 +1217,7 @@ namespace spot
         return -1U;
       unsigned j = num_;
       num_ += num;
-      if (num_ > 8 * sizeof(mark_t::value_t))
+      if (num_ > SPOT_NB_ACC)
         throw std::runtime_error("Too many acceptance sets used.");
       all_ = all_sets_();
       return j;
@@ -1340,7 +1355,7 @@ namespace spot
   protected:
     mark_t all_sets_() const
     {
-      return mark_t::all() >> (8*sizeof(mark_t::value_t) - num_);
+      return mark_t::all() >> (SPOT_NB_ACC - num_);
     }
 
     unsigned num_;
@@ -1519,8 +1534,7 @@ namespace std
   {
     size_t operator()(spot::acc_cond::mark_t m) const noexcept
     {
-      std::hash<decltype(m.id)> h;
-      return h(m.id);
+      return m.hash();
     }
   };
 }