diff --git a/CHANGELOG.md b/CHANGELOG.md
index 5425c5d3..1a52aac0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,6 +8,7 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/).
 ### Changed
 
 - Using absolute instead of relative imports ([[#995](https://github.com/pdfminer/pdfminer.six/pull/995)])
+- Allow suppression of `(cid:N)` in `pdf2txt.py` ([#1070](https://github.com/pdfminer/pdfminer.six/pull/1070))
 
 ### Deprecated
 
diff --git a/samples/contrib/issue-1056-cid.pdf b/samples/contrib/issue-1056-cid.pdf
new file mode 100644
index 00000000..76c610a6
Binary files /dev/null and b/samples/contrib/issue-1056-cid.pdf differ
diff --git a/tests/test_tools_pdf2txt.py b/tests/test_tools_pdf2txt.py
index e80a5e69..ec0be9be 100644
--- a/tests/test_tools_pdf2txt.py
+++ b/tests/test_tools_pdf2txt.py
@@ -68,6 +68,21 @@ def test_contrib_issue_350(self):
         """
         run("contrib/issue-00352-asw-oct96-p41.pdf")
 
+    def test_contrib_issue_1056(self):
+        """Test fix to pdf2txt.py mentioned in
+        https://github.com/pdfminer/pdfminer.six/issues/1056"""
+        with TemporaryFilePath() as output_file_name:
+            pdf2txt.main(
+                [
+                    "--ignore-unmapped",
+                    f"-o{output_file_name}",
+                    absolute_sample_path("contrib/issue-1056-cid.pdf"),
+                ]
+            )
+            with open(output_file_name) as infh:
+                for spam in infh:
+                    assert "(cid:" not in spam
+
     def test_scancode_patchelf(self):
         """Regression test for https://github.com/euske/pdfminer/issues/96"""
         run("scancode/patchelf.pdf")
diff --git a/tools/pdf2txt.py b/tools/pdf2txt.py
index 3341690c..8344b1d8 100755
--- a/tools/pdf2txt.py
+++ b/tools/pdf2txt.py
@@ -9,6 +9,7 @@
 from typing import Any, Container, Iterable, List, Optional
 
 import pdfminer.high_level
+from pdfminer.converter import PDFLayoutAnalyzer
 from pdfminer.layout import LAParams
 from pdfminer.pdfexceptions import PDFValueError
 from pdfminer.utils import AnyIO
@@ -277,6 +278,13 @@ def create_parser() -> argparse.ArgumentParser:
         help="Remove control statement from text. "
         "Only used when output_type is xml.",
     )
+    output_params.add_argument(
+        "--ignore-unmapped",
+        "-I",
+        default=False,
+        action="store_true",
+        help="Ignore unmapped characters rather than outputting" "(cid:N) in the text",
+    )
 
     return parser
 
@@ -309,6 +317,9 @@ def parse_args(args: Optional[List[str]]) -> argparse.Namespace:
             if parsed_args.outfile.endswith(override):
                 parsed_args.output_type = alttype
 
+    if parsed_args.ignore_unmapped:
+        PDFLayoutAnalyzer.handle_undefined_char = lambda *args: ""  # type: ignore
+
     return parsed_args