diff --git a/Lib/decimal.py b/Lib/decimal.py
index 727aee2f108..64808806d37 100644
--- a/Lib/decimal.py
+++ b/Lib/decimal.py
@@ -1655,47 +1655,53 @@ class Decimal(object):
         exp_min = len(self._int) + self._exp - context.prec
         if exp_min > Etop:
             # overflow: exp_min > Etop iff self.adjusted() > Emax
+            ans = context._raise_error(Overflow, 'above Emax', self._sign)
             context._raise_error(Inexact)
             context._raise_error(Rounded)
-            return context._raise_error(Overflow, 'above Emax', self._sign)
+            return ans
+
         self_is_subnormal = exp_min < Etiny
         if self_is_subnormal:
-            context._raise_error(Subnormal)
             exp_min = Etiny
 
         # round if self has too many digits
         if self._exp < exp_min:
-            context._raise_error(Rounded)
             digits = len(self._int) + self._exp - exp_min
             if digits < 0:
                 self = _dec_from_triple(self._sign, '1', exp_min-1)
                 digits = 0
-            this_function = getattr(self, self._pick_rounding_function[context.rounding])
-            changed = this_function(digits)
+            rounding_method = self._pick_rounding_function[context.rounding]
+            changed = getattr(self, rounding_method)(digits)
             coeff = self._int[:digits] or '0'
-            if changed == 1:
+            if changed > 0:
                 coeff = str(int(coeff)+1)
-            ans = _dec_from_triple(self._sign, coeff, exp_min)
+                if len(coeff) > context.prec:
+                    coeff = coeff[:-1]
+                    exp_min += 1
 
+            # check whether the rounding pushed the exponent out of range
+            if exp_min > Etop:
+                ans = context._raise_error(Overflow, 'above Emax', self._sign)
+            else:
+                ans = _dec_from_triple(self._sign, coeff, exp_min)
+
+            # raise the appropriate signals, taking care to respect
+            # the precedence described in the specification
+            if changed and self_is_subnormal:
+                context._raise_error(Underflow)
+            if self_is_subnormal:
+                context._raise_error(Subnormal)
             if changed:
                 context._raise_error(Inexact)
-                if self_is_subnormal:
-                    context._raise_error(Underflow)
-                    if not ans:
-                        # raise Clamped on underflow to 0
-                        context._raise_error(Clamped)
-                elif len(ans._int) == context.prec+1:
-                    # we get here only if rescaling rounds the
-                    # cofficient up to exactly 10**context.prec
-                    if ans._exp < Etop:
-                        ans = _dec_from_triple(ans._sign,
-                                                   ans._int[:-1], ans._exp+1)
-                    else:
-                        # Inexact and Rounded have already been raised
-                        ans = context._raise_error(Overflow, 'above Emax',
-                                                   self._sign)
+            context._raise_error(Rounded)
+            if not ans:
+                # raise Clamped on underflow to 0
+                context._raise_error(Clamped)
             return ans
 
+        if self_is_subnormal:
+            context._raise_error(Subnormal)
+
         # fold down if _clamp == 1 and self has too few digits
         if context._clamp == 1 and self._exp > Etop:
             context._raise_error(Clamped)
@@ -2322,6 +2328,7 @@ class Decimal(object):
         # from here on, the result always goes through the call
         # to _fix at the end of this function.
         ans = None
+        exact = False
 
         # crude test to catch cases of extreme overflow/underflow.  If
         # log10(self)*other >= 10**bound and bound >= len(str(Emax))
@@ -2346,6 +2353,7 @@ class Decimal(object):
             ans = self._power_exact(other, context.prec + 1)
             if ans is not None and result_sign == 1:
                 ans = _dec_from_triple(1, ans._int, ans._exp)
+            exact = True
 
         # usual case: inexact result, x**y computed directly as exp(y*log(x))
         if ans is None:
@@ -2368,24 +2376,55 @@ class Decimal(object):
 
             ans = _dec_from_triple(result_sign, str(coeff), exp)
 
-        # the specification says that for non-integer other we need to
-        # raise Inexact, even when the result is actually exact.  In
-        # the same way, we need to raise Underflow here if the result
-        # is subnormal.  (The call to _fix will take care of raising
-        # Rounded and Subnormal, as usual.)
-        if not other._isinteger():
-            context._raise_error(Inexact)
-            # pad with zeros up to length context.prec+1 if necessary
+        # unlike exp, ln and log10, the power function respects the
+        # rounding mode; no need to switch to ROUND_HALF_EVEN here
+
+        # There's a difficulty here when 'other' is not an integer and
+        # the result is exact.  In this case, the specification
+        # requires that the Inexact flag be raised (in spite of
+        # exactness), but since the result is exact _fix won't do this
+        # for us.  (Correspondingly, the Underflow signal should also
+        # be raised for subnormal results.)  We can't directly raise
+        # these signals either before or after calling _fix, since
+        # that would violate the precedence for signals.  So we wrap
+        # the ._fix call in a temporary context, and reraise
+        # afterwards.
+        if exact and not other._isinteger():
+            # pad with zeros up to length context.prec+1 if necessary; this
+            # ensures that the Rounded signal will be raised.
             if len(ans._int) <= context.prec:
-                expdiff = context.prec+1 - len(ans._int)
+                expdiff = context.prec + 1 - len(ans._int)
                 ans = _dec_from_triple(ans._sign, ans._int+'0'*expdiff,
                                        ans._exp-expdiff)
-            if ans.adjusted() < context.Emin:
-                context._raise_error(Underflow)
 
-        # unlike exp, ln and log10, the power function respects the
-        # rounding mode; no need to use ROUND_HALF_EVEN here
-        ans = ans._fix(context)
+            # create a copy of the current context, with cleared flags/traps
+            newcontext = context.copy()
+            newcontext.clear_flags()
+            for exception in _signals:
+                newcontext.traps[exception] = 0
+
+            # round in the new context
+            ans = ans._fix(newcontext)
+
+            # raise Inexact, and if necessary, Underflow
+            newcontext._raise_error(Inexact)
+            if newcontext.flags[Subnormal]:
+                newcontext._raise_error(Underflow)
+
+            # propagate signals to the original context; _fix could
+            # have raised any of Overflow, Underflow, Subnormal,
+            # Inexact, Rounded, Clamped.  Overflow needs the correct
+            # arguments.  Note that the order of the exceptions is
+            # important here.
+            if newcontext.flags[Overflow]:
+                context._raise_error(Overflow, 'above Emax', ans._sign)
+            for exception in Underflow, Subnormal, Inexact, Rounded, Clamped:
+                if newcontext.flags[exception]:
+                    context._raise_error(exception)
+
+        else:
+            ans = ans._fix(context)
+
         return ans
 
     def __rpow__(self, other, context=None):
@@ -2479,14 +2518,15 @@ class Decimal(object):
                                         'quantize result has too many digits for current context')
 
         # raise appropriate flags
-        if ans._exp > self._exp:
-            context._raise_error(Rounded)
-            if ans != self:
-                context._raise_error(Inexact)
         if ans and ans.adjusted() < context.Emin:
             context._raise_error(Subnormal)
+        if ans._exp > self._exp:
+            if ans != self:
+                context._raise_error(Inexact)
+            context._raise_error(Rounded)
 
-        # call to fix takes care of any necessary folddown
+        # call to fix takes care of any necessary folddown, and
+        # signals Clamped if necessary
         ans = ans._fix(context)
         return ans
 
@@ -2585,10 +2625,10 @@ class Decimal(object):
             context = getcontext()
         if rounding is None:
             rounding = context.rounding
-        context._raise_error(Rounded)
         ans = self._rescale(0, rounding)
         if ans != self:
             context._raise_error(Inexact)
+        context._raise_error(Rounded)
         return ans
 
     def to_integral_value(self, rounding=None, context=None):
@@ -3469,13 +3509,13 @@ class Decimal(object):
             context._raise_error(Overflow,
                                  'Infinite result from next_toward',
                                  ans._sign)
-            context._raise_error(Rounded)
             context._raise_error(Inexact)
+            context._raise_error(Rounded)
         elif ans.adjusted() < context.Emin:
             context._raise_error(Underflow)
             context._raise_error(Subnormal)
-            context._raise_error(Rounded)
             context._raise_error(Inexact)
+            context._raise_error(Rounded)
             # if precision == 1 then we don't raise Clamped for a
             # result 0E-Etiny.
             if not ans:
diff --git a/Lib/test/test_decimal.py b/Lib/test/test_decimal.py
index d6e170d1e41..21590880b08 100644
--- a/Lib/test/test_decimal.py
+++ b/Lib/test/test_decimal.py
@@ -41,6 +41,12 @@ except ImportError:
 # Useful Test Constant
 Signals = tuple(getcontext().flags.keys())
 
+# Signals ordered with respect to precedence: when an operation
+# produces multiple signals, signals occurring later in the list
+# should be handled before those occurring earlier in the list.
+OrderedSignals = (Clamped, Rounded, Inexact, Subnormal,
+                  Underflow, Overflow, DivisionByZero, InvalidOperation)
+
 # Tests are built around these assumed context defaults.
 # test_main() restores the original context.
 def init():
@@ -351,6 +357,25 @@ class DecimalTest(unittest.TestCase):
                 else:
                     self.fail("Did not raise %s in %s" % (error, s))
                 self.context.traps[error] = 0
+
+            # as above, but add traps cumulatively, to check precedence
+            ordered_errors = [e for e in OrderedSignals if e in theirexceptions]
+            for error in ordered_errors:
+                self.context.traps[error] = 1
+                try:
+                    funct(*vals)
+                except error:
+                    pass
+                except Signals as e:
+                    self.fail("Raised %s in %s; expected %s" %
+                              (type(e), s, error))
+                else:
+                    self.fail("Did not raise %s in %s" % (error, s))
+            # reset traps
+            for error in ordered_errors:
+                self.context.traps[error] = 0
+
+
         if DEBUG:
             print("--", self.context)
         try:
diff --git a/Misc/NEWS b/Misc/NEWS
index 6b4f316b5f0..e847c01e5be 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -348,6 +348,12 @@ C-API
 Library
 -------
 
+- Issue #8567: Fix precedence of signals in Decimal module: when a
+  Decimal operation raises multiple signals and more than one of those
+  signals is trapped, the specification determines the order in which
+  the signals should be handled.  In many cases this order wasn't
+  being followed, leading to the wrong Python exception being raised.
+
 - Issue #7865: The close() method of :mod:`io` objects should not swallow
   exceptions raised by the implicit flush().  Also ensure that calling
   close() several times is supported.  Patch by Pascal Chambon.