diff --git a/h11/_events.py b/h11/_events.py
index 68f6034..e9c85b7 100644
--- a/h11/_events.py
+++ b/h11/_events.py
@@ -24,6 +24,7 @@ class _EventBundle(object):
     _defaults = {}
 
     def __init__(self, **kwargs):
+        _parsed = kwargs.pop("_parsed", False)
         allowed = set(self._fields)
         for kwarg in kwargs:
             if kwarg not in allowed:
@@ -42,15 +43,17 @@ def __init__(self, **kwargs):
         # Special handling for some fields
 
         if "headers" in self.__dict__:
-            self.headers = _headers.normalize_and_validate(self.headers)
+            self.headers = _headers.normalize_and_validate(
+                self.headers, _parsed=_parsed)
 
-        for field in ["method", "target", "http_version", "reason"]:
-            if field in self.__dict__:
-                self.__dict__[field] = bytesify(self.__dict__[field])
+        if not _parsed:
+            for field in ["method", "target", "http_version", "reason"]:
+                if field in self.__dict__:
+                    self.__dict__[field] = bytesify(self.__dict__[field])
 
-        if "status_code" in self.__dict__:
-            if not isinstance(self.status_code, int):
-                raise LocalProtocolError("status code must be integer")
+            if "status_code" in self.__dict__:
+                if not isinstance(self.status_code, int):
+                    raise LocalProtocolError("status code must be integer")
 
         self._validate()
 
diff --git a/h11/_headers.py b/h11/_headers.py
index 47de8dc..ff3b153 100644
--- a/h11/_headers.py
+++ b/h11/_headers.py
@@ -60,16 +60,20 @@
 _field_name_re = re.compile(field_name.encode("ascii"))
 _field_value_re = re.compile(field_value.encode("ascii"))
 
-def normalize_and_validate(headers):
+def normalize_and_validate(headers, _parsed=False):
     new_headers = []
     saw_content_length = False
     saw_transfer_encoding = False
     for name, value in headers:
-        name = bytesify(name).lower()
-        value = bytesify(value)
-        validate(_field_name_re, name, "Illegal header name {!r}", name)
-        validate(_field_value_re, value,
-                 "Illegal header value {!r}", value)
+        # For headers coming out of the parser, we can safely skip some steps,
+        # because it always returns bytes and has already run these regexes
+        # over the data:
+        if not _parsed:
+            name = bytesify(name)
+            value = bytesify(value)
+            validate(_field_name_re, name, "Illegal header name {!r}", name)
+            validate(_field_value_re, value, "Illegal header value {!r}", value)
+        name = name.lower()
         if name == b"content-length":
             if saw_content_length:
                 raise LocalProtocolError("multiple Content-Length headers")
diff --git a/h11/_readers.py b/h11/_readers.py
index 9ed0a1c..c7248fd 100644
--- a/h11/_readers.py
+++ b/h11/_readers.py
@@ -63,7 +63,9 @@ def maybe_read_from_IDLE_client(buf):
     if not lines:
         raise LocalProtocolError("no request line received")
     matches = validate(request_line_re, lines[0])
-    return Request(headers=list(_decode_header_lines(lines[1:])), **matches)
+    return Request(headers=list(_decode_header_lines(lines[1:])),
+                   _parsed=True,
+                   **matches)
 
 status_line_re = re.compile(status_line.encode("ascii"))
 
@@ -79,7 +81,9 @@ def maybe_read_from_SEND_RESPONSE_server(buf):
         matches["reason"] = b""
     status_code = matches["status_code"] = int(matches["status_code"])
     class_ = InformationalResponse if status_code < 200 else Response
-    return class_(headers=list(_decode_header_lines(lines[1:])), **matches)
+    return class_(headers=list(_decode_header_lines(lines[1:])),
+                  _parsed=True,
+                  **matches)
 
 
 class ContentLengthReader: