diff --git a/Lib/decimal.py b/Lib/decimal.py
index 6bd655b..b74ab01 100644
--- a/Lib/decimal.py
+++ b/Lib/decimal.py
@@ -1601,7 +1601,13 @@
 
     def __float__(self):
         """Float representation."""
-        return float(str(self))
+        if self._isnan():
+            if self.is_snan():
+                raise ValueError("Cannot convert signaling NaN to float")
+            s = "-nan" if self._sign else "nan"
+        else:
+            s = str(self)
+        return float(s)
 
     def __int__(self):
         """Converts self to an int, truncating if necessary."""
diff --git a/Lib/test/test_decimal.py b/Lib/test/test_decimal.py
index 781df1f..d00ed5a 100644
--- a/Lib/test/test_decimal.py
+++ b/Lib/test/test_decimal.py
@@ -1942,6 +1942,22 @@
         for d, n, r in test_triples:
             self.assertEqual(str(round(Decimal(d), n)), r)
 
+    def test_nan_to_float(self):
+        # Test conversions of decimal NANs to float.
+        # See http://bugs.python.org/issue15544
+        Decimal = self.decimal.Decimal
+        for s in ('nan', 'nan1234', '-nan', '-nan2468'):
+            f = float(Decimal(s))
+            self.assertTrue(math.isnan(f))
+            sign = math.copysign(1.0, f)
+            self.assertEqual(sign, -1.0 if s.startswith('-') else 1.0)
+
+    def test_snan_to_float(self):
+        Decimal = self.decimal.Decimal
+        for s in ('snan', '-snan', 'snan1357', '-snan1234'):
+            d = Decimal(s)
+            self.assertRaises(ValueError, float, d)
+
     def test_eval_round_trip(self):
         Decimal = self.decimal.Decimal
 
diff --git a/Misc/NEWS b/Misc/NEWS
index 6d046ff..3521001 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -32,6 +32,8 @@
 Library
 -------
 
+- Issue #15544: Fix Decimal.__float__ to work with payload-carrying NaNs.
+
 - Issue #15776: Allow pyvenv to work in existing directory with --clean.
 
 - Issue #15249: BytesGenerator now correctly mangles From lines (when
diff --git a/Modules/_decimal/_decimal.c b/Modules/_decimal/_decimal.c
index ecca411..15c64e2 100644
--- a/Modules/_decimal/_decimal.c
+++ b/Modules/_decimal/_decimal.c
@@ -3357,7 +3357,23 @@
 {
     PyObject *f, *s;
 
-    s = dec_str(dec);
+    if (mpd_isnan(MPD(dec))) {
+        if (mpd_issnan(MPD(dec))) {
+            PyErr_SetString(PyExc_ValueError,
+                "cannot convert signaling NaN to float");
+            return NULL;
+        }
+        if (mpd_isnegative(MPD(dec))) {
+            s = PyUnicode_FromString("-nan");
+        }
+        else {
+            s = PyUnicode_FromString("nan");
+        }
+    }
+    else {
+        s = dec_str(dec);
+    }
+
     if (s == NULL) {
         return NULL;
     }