diff --git a/flang/include/flang/Evaluate/real.h b/flang/include/flang/Evaluate/real.h
--- a/flang/include/flang/Evaluate/real.h
+++ b/flang/include/flang/Evaluate/real.h
@@ -177,17 +177,21 @@
   template <typename INT>
   ValueWithRealFlags<Real> SCALE(const INT &by,
       Rounding rounding = TargetCharacteristics::defaultRounding) const {
-    auto expo{exponentBias + by.ToInt64()};
+    // Normalize a fraction with just its LSB set and then multiply.
+    // (Set the LSB, not the MSB, in case the scale factor needs to
+    //  be subnormal.)
+    auto adjust{exponentBias + binaryPrecision - 1};
+    auto expo{adjust + by.ToInt64()};
     if (IsZero()) {
       expo = exponentBias; // ignore by, don't overflow
     } else if (by > INT{maxExponent}) {
-      expo = maxExponent;
-    } else if (by < INT{-exponentBias}) {
+      expo = maxExponent + binaryPrecision - 1;
+    } else if (by < INT{-adjust}) {
       expo = -1;
     }
     Real twoPow;
     RealFlags flags{
-        twoPow.Normalize(false, static_cast<int>(expo), Fraction::MASKL(1))};
+        twoPow.Normalize(false, static_cast<int>(expo), Fraction::MASKR(1))};
     ValueWithRealFlags<Real> result{Multiply(twoPow, rounding)};
     result.flags |= flags;
     return result;
diff --git a/flang/lib/Evaluate/real.cpp b/flang/lib/Evaluate/real.cpp
--- a/flang/lib/Evaluate/real.cpp
+++ b/flang/lib/Evaluate/real.cpp
@@ -765,9 +765,7 @@
   } else if (IsZero()) {
     return *this;
   } else {
-    Real result;
-    result.Normalize(IsNegative(), expo + exponentBias - 1, GetFraction());
-    return result;
+    return SCALE(Integer<32>(expo - UnbiasedExponent() - 1)).value;
   }
 }
 
diff --git a/flang/test/Evaluate/folding07.f90 b/flang/test/Evaluate/folding07.f90
--- a/flang/test/Evaluate/folding07.f90
+++ b/flang/test/Evaluate/folding07.f90
@@ -280,5 +280,6 @@
   logical, parameter :: test_set_exponent_0 = set_exponent(1., 0) == 0.5
   logical, parameter :: test_set_exponent_1 = set_exponent(1., 1) == 1.
   logical, parameter :: test_set_exponent_2 = set_exponent(1., 2) == 2.
+  logical, parameter :: test_set_exponent_min = set_exponent(1., -149) == 1.40129846432481707092372958328991613128026194187651577175706828388979108268586060148663818836212158203125e-45_4
 
 end module