diff -r 02a4f0cb8fed Lib/decimal.py
--- a/Lib/decimal.py	Sun May 22 15:27:14 2011 +0200
+++ b/Lib/decimal.py	Sun May 22 14:50:46 2011 +0100
@@ -2090,18 +2090,10 @@
                 # now xc is a power of 2; e is its exponent
                 e = _nbits(xc)-1
                 # find e*y and xe*y; both must be integers
-                if ye >= 0:
-                    y_as_int = yc*10**ye
-                    e = e*y_as_int
-                    xe = xe*y_as_int
-                else:
-                    ten_pow = 10**-ye
-                    e, remainder = divmod(e*yc, ten_pow)
-                    if remainder:
-                        return None
-                    xe, remainder = divmod(xe*yc, ten_pow)
-                    if remainder:
-                        return None
+                e = _decimal_lshift_exact(e * yc, ye)
+                xe = _decimal_lshift_exact(xe * yc, ye)
+                if e is None or xe is None:
+                    return None
 
                 if e*65 >= p*93: # 93/65 > log(10)/log(5)
                     return None
@@ -2117,18 +2109,11 @@
                 while xc % 5 == 0:
                     xc //= 5
                     e -= 1
-                if ye >= 0:
-                    y_as_integer = yc*10**ye
-                    e = e*y_as_integer
-                    xe = xe*y_as_integer
-                else:
-                    ten_pow = 10**-ye
-                    e, remainder = divmod(e*yc, ten_pow)
-                    if remainder:
-                        return None
-                    xe, remainder = divmod(xe*yc, ten_pow)
-                    if remainder:
-                        return None
+                e = _decimal_lshift_exact(e * yc, ye)
+                xe = _decimal_lshift_exact(xe * yc, ye)
+                if e is None or xe is None:
+                    return None
+
                 if e*3 >= p*10: # 10/3 > log(10)/log(2)
                     return None
                 xc = 2**e
@@ -5529,6 +5514,27 @@
 
 _nbits = int.bit_length
 
+def _decimal_lshift_exact(n, e):
+    """ Given integers n and e, return n * 10**e if it's an integer, else None.
+
+    The computation is designed to avoid computing large powers of 10
+    unnecessarily.
+
+    >>> _decimal_lshift_exact(3, 4)
+    30000
+    >>> _decimal_lshift_exact(300, -999999999)  # returns None
+
+    """
+    if n == 0:
+        return 0
+    elif e >= 0:
+        return n * 10**e
+    else:
+        # val_n = largest power of 10 dividing n.
+        str_n = str(abs(n))
+        val_n = len(str_n) - len(str_n.rstrip('0'))
+        return None if val_n < -e else n // 10**-e
+
 def _sqrt_nearest(n, a):
     """Closest integer to the square root of the positive integer n.  a is
     an initial approximation to the square root.  Any positive integer
diff -r 02a4f0cb8fed Lib/test/decimaltestdata/extra.decTest
--- a/Lib/test/decimaltestdata/extra.decTest	Sun May 22 15:27:14 2011 +0200
+++ b/Lib/test/decimaltestdata/extra.decTest	Sun May 22 14:50:46 2011 +0100
@@ -222,12 +222,25 @@
 extr1701 power 100.0 -557.71e-742888888 -> 1.000000000000000 Inexact Rounded
 extr1702 power 10 1e-100 -> 1.000000000000000 Inexact Rounded
 
+-- Another one (see issue #12080).  Thanks again to Stefan Krah.
+extr1703 power 4 -1.2e-999999999 -> 1.000000000000000 Inexact Rounded
+
 -- A couple of interesting exact cases for power.  Note that the specification
 -- requires these to be reported as Inexact.
 extr1710 power 1e375 56e-3 -> 1.000000000000000E+21 Inexact Rounded
 extr1711 power 10000 0.75 -> 1000.000000000000 Inexact Rounded
 extr1712 power 1e-24 0.875 -> 1.000000000000000E-21 Inexact Rounded
 
+-- Some more exact cases, exercising power with negative second argument.
+extr1720 power 400 -0.5 -> 0.05000000000000000 Inexact Rounded
+extr1721 power 4096 -0.75 -> 0.001953125000000000 Inexact Rounded
+extr1722 power 625e4 -0.25 -> 0.02000000000000000 Inexact Rounded
+
+-- Nonexact cases, to exercise some of the early exit conditions from
+-- _power_exact.
+extr1730 power 2048 -0.75 -> 0.003284751622084822 Inexact Rounded
+
+
 -- Tests for the is_* boolean operations
 precision: 9
 maxExponent: 999