diff --git a/fpu/softfloat-specialize.c.inc b/fpu/softfloat-specialize.c.inc
index 73789e97d7..8327f72786 100644
--- a/fpu/softfloat-specialize.c.inc
+++ b/fpu/softfloat-specialize.c.inc
@@ -237,16 +237,6 @@ floatx80 floatx80_default_inf(bool zSign, float_status *status)
     return packFloatx80(zSign, 0x7fff, z ? 0 : (1ULL << 63));
 }
 
-#define floatx80_infinity_high 0x7FFF
-#if defined(TARGET_M68K)
-#define floatx80_infinity_low  UINT64_C(0x0000000000000000)
-#else
-#define floatx80_infinity_low  UINT64_C(0x8000000000000000)
-#endif
-
-const floatx80 floatx80_infinity
-    = make_floatx80_init(floatx80_infinity_high, floatx80_infinity_low);
-
 /*----------------------------------------------------------------------------
 | Returns 1 if the half-precision floating-point value `a' is a quiet
 | NaN; otherwise returns 0.
diff --git a/include/fpu/softfloat-types.h b/include/fpu/softfloat-types.h
index dd22ecdbe6..e1732beba4 100644
--- a/include/fpu/softfloat-types.h
+++ b/include/fpu/softfloat-types.h
@@ -330,6 +330,11 @@ typedef enum __attribute__((__packed__)) {
 typedef enum __attribute__((__packed__)) {
     /* In the default Infinity value, is the Integer bit 0 ? */
     floatx80_default_inf_int_bit_is_zero = 1,
+    /*
+     * Are Pseudo-infinities (Inf with the Integer bit zero) valid?
+     * If so, floatx80_is_infinity() will return true for them.
+     */
+    floatx80_pseudo_inf_valid = 2,
 } FloatX80Behaviour;
 
 /*
diff --git a/include/fpu/softfloat.h b/include/fpu/softfloat.h
index 3c83d703ba..07259c5930 100644
--- a/include/fpu/softfloat.h
+++ b/include/fpu/softfloat.h
@@ -960,7 +960,6 @@ float128 floatx80_to_float128(floatx80, float_status *status);
 /*----------------------------------------------------------------------------
 | The pattern for an extended double-precision inf.
 *----------------------------------------------------------------------------*/
-extern const floatx80 floatx80_infinity;
 floatx80 floatx80_default_inf(bool zSign, float_status *status);
 
 /*----------------------------------------------------------------------------
@@ -998,12 +997,17 @@ static inline floatx80 floatx80_chs(floatx80 a)
 
 static inline bool floatx80_is_infinity(floatx80 a, float_status *status)
 {
-#if defined(TARGET_M68K)
-    return (a.high & 0x7fff) == floatx80_infinity.high && !(a.low << 1);
-#else
-    return (a.high & 0x7fff) == floatx80_infinity.high &&
-                       a.low == floatx80_infinity.low;
-#endif
+    /*
+     * It's target-specific whether the Integer bit is permitted
+     * to be 0 in a valid Infinity value. (x86 says no, m68k says yes).
+     */
+    bool intbit = a.low >> 63;
+
+    if (!intbit &&
+        !(status->floatx80_behaviour & floatx80_pseudo_inf_valid)) {
+        return false;
+    }
+    return (a.high & 0x7fff) == 0x7fff && !(a.low << 1);
 }
 
 static inline bool floatx80_is_neg(floatx80 a)
diff --git a/target/m68k/cpu.c b/target/m68k/cpu.c
index df66e8ba22..56b23de21f 100644
--- a/target/m68k/cpu.c
+++ b/target/m68k/cpu.c
@@ -110,8 +110,10 @@ static void m68k_cpu_reset_hold(Object *obj, ResetType type)
     /*
      * m68k-specific floatx80 behaviour:
      *  * default Infinity values have a zero Integer bit
+     *  * input Infinities may have the Integer bit either 0 or 1
      */
-    set_floatx80_behaviour(floatx80_default_inf_int_bit_is_zero,
+    set_floatx80_behaviour(floatx80_default_inf_int_bit_is_zero |
+                           floatx80_pseudo_inf_valid,
                            &env->fp_status);
 
     nan = floatx80_default_nan(&env->fp_status);