diff --git a/src/mdformat/_api.py b/src/mdformat/_api.py
index 18ec9e5..bffa4c2 100644
--- a/src/mdformat/_api.py
+++ b/src/mdformat/_api.py
@@ -7,13 +7,7 @@
 from typing import Any
 
 from mdformat._conf import DEFAULT_OPTS
-from mdformat._util import (
-    EMPTY_MAP,
-    NULL_CTX,
-    atomic_write,
-    build_mdit,
-    detect_newline_type,
-)
+from mdformat._util import EMPTY_MAP, NULL_CTX, build_mdit, detect_newline_type
 from mdformat.renderer import MDRenderer
 
 
@@ -75,4 +69,6 @@ def file(
     newline = detect_newline_type(
         original_md, options.get("end_of_line", DEFAULT_OPTS["end_of_line"])
     )
-    atomic_write(f, formatted_md, newline)
+    formatted_md = formatted_md.replace("\n", newline)
+    if formatted_md != original_md:
+        f.write_bytes(formatted_md.encode())
diff --git a/src/mdformat/_cli.py b/src/mdformat/_cli.py
index 2e282d0..39491cd 100644
--- a/src/mdformat/_cli.py
+++ b/src/mdformat/_cli.py
@@ -6,7 +6,6 @@
 import itertools
 import logging
 from pathlib import Path
-import re
 import shutil
 import sys
 import textwrap
@@ -14,13 +13,10 @@
 import mdformat
 from mdformat._compat import importlib_metadata
 from mdformat._conf import DEFAULT_OPTS, InvalidConfError, read_toml_opts
-from mdformat._util import atomic_write, detect_newline_type, is_md_equal
+from mdformat._util import detect_newline_type, is_md_equal
 import mdformat.plugins
 import mdformat.renderer
 
-# Match "\r" and "\n" characters that are not part of a "\r\n" sequence
-RE_NON_CRLF_LINE_END = re.compile(r"(?:[^\r]|^)\n|\r(?:[^\n]|\Z)")
-
 
 class RendererWarningPrinter(logging.Handler):
     def emit(self, record: logging.LogRecord) -> None:
@@ -82,14 +78,10 @@ def run(cli_args: Sequence[str]) -> int:  # noqa: C901
             _filename=path_str,
         )
         newline = detect_newline_type(original_str, opts["end_of_line"])
+        formatted_str = formatted_str.replace("\n", newline)
 
         if opts["check"]:
-            original_str_lf_eol = original_str.replace("\r\n", "\n").replace("\r", "\n")
-            if (
-                (formatted_str != original_str_lf_eol)
-                or (newline == "\n" and "\r" in original_str)
-                or (newline == "\r\n" and RE_NON_CRLF_LINE_END.search(original_str))
-            ):
+            if formatted_str != original_str:
                 format_errors_found = True
                 print_error(f'File "{path_str}" is not formatted.')
         else:
@@ -111,12 +103,10 @@ def run(cli_args: Sequence[str]) -> int:  # noqa: C901
                 )
                 return 1
             if path:
-                atomic_write(path, formatted_str, newline)
+                if formatted_str != original_str:
+                    path.write_bytes(formatted_str.encode())
             else:
-                with open(
-                    sys.stdout.fileno(), "w", closefd=False, newline=newline
-                ) as stdout:
-                    stdout.write(formatted_str)
+                sys.stdout.buffer.write(formatted_str.encode())
     if format_errors_found:
         return 1
     return 0
diff --git a/src/mdformat/_util.py b/src/mdformat/_util.py
index e711fdf..a4d634f 100644
--- a/src/mdformat/_util.py
+++ b/src/mdformat/_util.py
@@ -2,11 +2,7 @@
 
 from collections.abc import Iterable, Mapping
 from contextlib import nullcontext
-import filecmp
-import os
-from pathlib import Path
 import re
-import tempfile
 from types import MappingProxyType
 from typing import Any, Literal
 
@@ -106,26 +102,6 @@ def is_md_equal(
     return html_texts["md1"] == html_texts["md2"]
 
 
-def atomic_write(path: Path, text: str, newline: str) -> None:
-    """A function for atomic writes to a file.
-
-    Writes a temporary file first and then replaces the original file
-    with the temporary one. This is to avoid a moment where only empty
-    or partial content exists on disk.
-    """
-    fd, tmp_path = tempfile.mkstemp(dir=path.parent)
-    try:
-        with open(fd, "w", encoding="utf-8", newline=newline) as f:
-            f.write(text)
-        if filecmp.cmp(tmp_path, path, shallow=False):
-            os.remove(tmp_path)
-        else:
-            os.replace(tmp_path, path)
-    except BaseException:  # pragma: no cover
-        os.remove(tmp_path)
-        raise
-
-
 def detect_newline_type(md: str, eol_setting: str) -> Literal["\n", "\r\n"]:
     """Returns the newline-character to be used for output.