diff --git a/include/fmt/format.h b/include/fmt/format.h
index 2b7a933f..b3e3fb86 100644
--- a/include/fmt/format.h
+++ b/include/fmt/format.h
@@ -3254,7 +3254,13 @@ FMT_CONSTEXPR20 inline void format_dragon(basic_fp<uint128_t> value,
   if (!upper) upper = &lower;
   bool shortest = num_digits < 0;
   if ((flags & dragon::fixup) != 0) {
-    if (add_compare(numerator, *upper, denominator) + even <= 0) {
+    // In the shortest mode the upper boundary is included because the output
+    // may round up to the next power of 10. With a given number of digits,
+    // rounding happens after digit generation, so only the value is compared.
+    bool too_high =
+        shortest ? add_compare(numerator, *upper, denominator) + even <= 0
+                 : compare(numerator, denominator) < 0;
+    if (too_high) {
       --exp10;
       numerator *= 10;
       if (num_digits < 0) {
diff --git a/test/format-test.cc b/test/format-test.cc
index c61d2ce4..19f1fd52 100644
--- a/test/format-test.cc
+++ b/test/format-test.cc
@@ -1283,6 +1283,16 @@ TEST(format_test, precision) {
     EXPECT_EQ(
         fmt::format("{:0g}", std::numeric_limits<long double>::denorm_min()),
         "3.6452e-4951");
+
+    // Values just below a power of 10 where the initial exponent estimate is
+    // one too high.
+    ld = std::ldexp(static_cast<long double>(0x83126e978d4fdf3bULL), -73);
+    EXPECT_EQ(fmt::format("{:.20e}", ld), "9.99999999999999999958e-04");
+    ld = std::ldexp(static_cast<long double>(0xe596b7b0c643c719ULL), 79);
+    EXPECT_EQ(fmt::format("{:.0f}", ld),
+              "9999999999999999999741184793924429452148736");
+    EXPECT_EQ(fmt::format("{:.19e}", ld), "9.9999999999999999997e+42");
+    EXPECT_EQ(fmt::format("{:.21g}", ld), "9.99999999999999999974e+42");
   }
 
   EXPECT_EQ(fmt::format("{:#.0f}", 123.0), "123.");