diff --git a/idna/core.py b/idna/core.py
index 9115f12..afe942c 100644
--- a/idna/core.py
+++ b/idna/core.py
@@ -9,7 +9,8 @@
 _virama_combining_class = 9
 _alabel_prefix = b"xn--"
 _unicode_dots_re = re.compile("[\u002e\u3002\uff0e\uff61]")
-
+_ldh = (48,49,50,51,52,53,54,55,56,57,95,97,98,99,100,101,102,103,104,105,106,107,108,109,110,
+        111,112,113,114,115,116,117,118,119,120,121,122)
 
 class IDNAError(UnicodeError):
     """Base exception for all IDNA-encoding related problems"""
@@ -341,16 +342,18 @@ def uts46_remap(domain: str, std3_rules: bool = True, transitional: bool = False
             uts46row = uts46data[code_point if code_point < 256 else bisect.bisect_left(uts46data, (code_point, "Z")) - 1]
             status = uts46row[1]
             replacement: Optional[str] = None
+            if std3_rules and code_point <= 0x7f:
+                if not code_point in _ldh:
+                    raise InvalidCodepoint("Codepoint {} at position {} does not follow STD3 rules".format(_unot(code_point), pos + 1))
             if len(uts46row) == 3:
                 replacement = uts46row[2]
             if (
                 status == "V"
                 or (status == "D" and not transitional)
-                or (status == "3" and not std3_rules and replacement is None)
             ):
                 output += char
             elif replacement is not None and (
-                status == "M" or (status == "3" and not std3_rules) or (status == "D" and transitional)
+                status == "M" or (status == "D" and transitional)
             ):
                 output += replacement
             elif status != "I":