diff --git a/Lib/decimal.py b/Lib/decimal.py
index 591f4dee3fe..b5a9435c9c7 100644
--- a/Lib/decimal.py
+++ b/Lib/decimal.py
@@ -2430,10 +2430,10 @@ class Decimal(object):
             sn = self._isnan()
             on = other._isnan()
             if sn or on:
-                if on == 1 and sn != 2:
-                    return self._fix_nan(context)
-                if sn == 1 and on != 2:
-                    return other._fix_nan(context)
+                if on == 1 and sn == 0:
+                    return self._fix(context)
+                if sn == 1 and on == 0:
+                    return other._fix(context)
                 return self._check_nans(other, context)
 
         c = self.__cmp__(other)
@@ -2472,10 +2472,10 @@ class Decimal(object):
             sn = self._isnan()
             on = other._isnan()
             if sn or on:
-                if on == 1 and sn != 2:
-                    return self._fix_nan(context)
-                if sn == 1 and on != 2:
-                    return other._fix_nan(context)
+                if on == 1 and sn == 0:
+                    return self._fix(context)
+                if sn == 1 and on == 0:
+                    return other._fix(context)
                 return self._check_nans(other, context)
 
         c = self.__cmp__(other)
@@ -3043,10 +3043,10 @@ class Decimal(object):
             sn = self._isnan()
             on = other._isnan()
             if sn or on:
-                if on == 1 and sn != 2:
-                    return self._fix_nan(context)
-                if sn == 1 and on != 2:
-                    return other._fix_nan(context)
+                if on == 1 and sn == 0:
+                    return self._fix(context)
+                if sn == 1 and on == 0:
+                    return other._fix(context)
                 return self._check_nans(other, context)
 
         c = self.copy_abs().__cmp__(other.copy_abs())
@@ -3073,10 +3073,10 @@ class Decimal(object):
             sn = self._isnan()
             on = other._isnan()
             if sn or on:
-                if on == 1 and sn != 2:
-                    return self._fix_nan(context)
-                if sn == 1 and on != 2:
-                    return other._fix_nan(context)
+                if on == 1 and sn == 0:
+                    return self._fix(context)
+                if sn == 1 and on == 0:
+                    return other._fix(context)
                 return self._check_nans(other, context)
 
         c = self.copy_abs().__cmp__(other.copy_abs())
diff --git a/Lib/test/decimaltestdata/extra.decTest b/Lib/test/decimaltestdata/extra.decTest
index 0cc1bbb5113..2e3fce85585 100644
--- a/Lib/test/decimaltestdata/extra.decTest
+++ b/Lib/test/decimaltestdata/extra.decTest
@@ -154,6 +154,23 @@ extr1301 fma Inf 0 sNaN456 -> NaN Invalid_operation
 extr1302 fma 0E123 -Inf sNaN789 -> NaN Invalid_operation
 extr1302 fma -Inf 0E-456 sNaN148 -> NaN Invalid_operation
 
+-- max/min/max_mag/min_mag bug in 2.5.2/2.6/3.0: max(NaN, finite) gave
+-- incorrect answers when the finite number required rounding; similarly
+-- for the other thre functions
+maxexponent: 999
+minexponent: -999
+precision: 6
+rounding: half_even
+extr1400 max NaN 1234567 -> 1.23457E+6 Inexact Rounded
+extr1401 max 3141590E-123 NaN1729 -> 3.14159E-117 Rounded
+extr1402 max -7.654321 -NaN -> -7.65432 Inexact Rounded
+extr1410 min -NaN -765432.1 -> -765432 Inexact Rounded
+extr1411 min 3141592 NaN -> 3.14159E+6 Inexact Rounded
+extr1420 max_mag 0.1111111 -NaN123 -> 0.111111 Inexact Rounded
+extr1421 max_mag NaN999999999 0.001234567 -> 0.00123457 Inexact Rounded
+extr1430 min_mag 9181716151 -NaN -> 9.18172E+9 Inexact Rounded
+extr1431 min_mag NaN4 1.818180E100 -> 1.81818E+100 Rounded
+
 -- Tests for the is_* boolean operations
 precision: 9
 maxExponent: 999
diff --git a/Misc/NEWS b/Misc/NEWS
index 518f355e546..6b7aa3aba50 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -107,6 +107,10 @@ Core and builtins
 Library
 -------
 
+- Issue #4084: Fix max, min, max_mag and min_mag Decimal methods to
+  give correct results in the case where one argument is a quiet NaN
+  and the other is a finite number that requires rounding.
+
 - Issue #1776581 and #4302. Minor corrections to smtplib.
 
 - Issue #3774: Fixed an error when create a Tkinter menu item without command