diff --git a/src/dir_diff.rs b/src/dir_diff.rs
index a7a8505..d8d90da 100644
--- a/src/dir_diff.rs
+++ b/src/dir_diff.rs
@@ -6,6 +6,7 @@
 //! Comparison of two directories, entry by entry, descending into
 //! subdirectories with `-r`.
 
+use std::borrow::Cow;
 use std::cmp::Ordering;
 use std::ffi::{OsStr, OsString};
 use std::fs::{self, Metadata};
@@ -14,7 +15,9 @@ use std::path::{Path, PathBuf};
 
 use crate::diff::{compare_files, Outcome};
 use crate::params::{MissingFile, Params};
-use crate::utils::{quote_file_name, quote_shell_argument, report_failure_to_read_input_file};
+use crate::utils::{
+    fold_file_name_case, quote_file_name, quote_shell_argument, report_failure_to_read_input_file,
+};
 
 /// Compares the directories `params.from` and `params.to`. `option_args` are
 /// the command line options, repeated in the header printed before the
@@ -59,14 +62,21 @@ impl DirectoryWalker<'_> {
             }
             canonical_dirs.push(canonical);
         }
-        let (Some(from_names), Some(to_names)) = (self.list(from_dir), self.list(to_dir)) else {
+        let (Some(mut from_names), Some(mut to_names)) = (self.list(from_dir), self.list(to_dir))
+        else {
             return Outcome::Trouble;
         };
+        // -S only applies to the operands, not to their subdirectories.
+        if let (true, Some(start)) = (self.ancestors.is_empty(), &self.params.starting_file) {
+            let start = self.name_key(start).into_owned();
+            from_names.retain(|name| *self.name_key(name) >= *start);
+            to_names.retain(|name| *self.name_key(name) >= *start);
+        }
         let ancestors_len = self.ancestors.len();
         self.ancestors.extend(canonical_dirs);
 
         let entries = pair_entries(&from_names, &to_names, |from, to| {
-            from.as_encoded_bytes().cmp(to.as_encoded_bytes())
+            self.name_key(from).cmp(&self.name_key(to))
         });
         for entry in entries {
             let entry_outcome = match entry {
@@ -117,9 +127,23 @@ impl DirectoryWalker<'_> {
             }
         }
         names.sort_unstable_by(|a, b| a.as_encoded_bytes().cmp(b.as_encoded_bytes()));
+        if self.params.ignore_file_name_case {
+            // A stable sort, so names equal ignoring case stay in byte order.
+            names.sort_by_cached_key(|name| fold_file_name_case(name));
+        }
         Some(names)
     }
 
+    /// Returns what entry names are sorted and matched by: the names
+    /// themselves, or their lowercase form with --ignore-file-name-case.
+    fn name_key<'n>(&self, name: &'n OsStr) -> Cow<'n, [u8]> {
+        if self.params.ignore_file_name_case {
+            Cow::Owned(fold_file_name_case(name))
+        } else {
+            Cow::Borrowed(name.as_encoded_bytes())
+        }
+    }
+
     /// Compares two entries of the compared directories, one of which may be
     /// missing when missing files are treated as empty.
     fn compare_entries(&mut self, from: &OsStr, to: &OsStr) -> Outcome {
diff --git a/src/params.rs b/src/params.rs
index d92346f..81b7048 100644
--- a/src/params.rs
+++ b/src/params.rs
@@ -1,11 +1,12 @@
-use std::ffi::OsString;
+use std::ffi::{OsStr, OsString};
 use std::iter::Peekable;
-use std::path::PathBuf;
+use std::path::{Path, PathBuf};
 
 use regex::Regex;
 
 use crate::bre::Bre;
 use crate::color::ColorWhen;
+use crate::utils::fold_file_name_case;
 
 #[derive(Clone, Copy, Debug, Default, Eq, PartialEq)]
 pub enum Format {
@@ -52,6 +53,10 @@ pub struct Params {
     /// headers (`-F` and `-p`).
     pub function_line_patterns: Vec<Bre>,
     pub recursive: bool,
+    /// The name from which to start comparing the top-level directories
+    /// (`-S`).
+    pub starting_file: Option<OsString>,
+    pub ignore_file_name_case: bool,
 }
 
 /// The pattern of `-p`, matching the first line of C functions.
@@ -77,6 +82,8 @@ impl Default for Params {
             presume_output_tty: false,
             function_line_patterns: Vec::new(),
             recursive: false,
+            starting_file: None,
+            ignore_file_name_case: false,
         }
     }
 }
@@ -175,23 +182,21 @@ pub fn parse_params<I: Iterator<Item = OsString>>(
             push_function_line_pattern(&mut params, C_FUNCTION_PATTERN)?;
             continue;
         }
-        let attached_function_line = param.to_str().and_then(|p| {
-            p.strip_prefix("--show-function-line=")
-                .or_else(|| p.strip_prefix("-F").filter(|pattern| !pattern.is_empty()))
-        });
-        if let Some(pattern) = attached_function_line {
-            push_function_line_pattern(&mut params, pattern)?;
+        if let Some(argument) = option_argument(&param, "-F", "--show-function-line") {
+            let pattern = argument_value(argument, &param, &mut opts)?;
+            push_function_line_pattern(&mut params, &pattern.to_string_lossy())?;
             continue;
         }
-        if param == "-F" || param == "--show-function-line" {
-            let Some(pattern) = next_param.map(|p| p.to_string_lossy().into_owned()) else {
-                return Err(format!(
-                    "option '{}' requires an argument",
-                    param.to_string_lossy()
-                ));
-            };
-            opts.next();
-            push_function_line_pattern(&mut params, &pattern)?;
+        if param == "--ignore-file-name-case" {
+            params.ignore_file_name_case = true;
+            continue;
+        }
+        if param == "--no-ignore-file-name-case" {
+            params.ignore_file_name_case = false;
+            continue;
+        }
+        if let Some(argument) = option_argument(&param, "-S", "--starting-file") {
+            params.starting_file = Some(argument_value(argument, &param, &mut opts)?);
             continue;
         }
         if param == "-r" || param == "--recursive" {
@@ -353,10 +358,12 @@ pub fn parse_params<I: Iterator<Item = OsString>>(
     let mut to_path: PathBuf = PathBuf::from(&params.to);
 
     if from_path.is_dir() && to_path.is_file() {
-        from_path.push(to_path.file_name().unwrap());
+        let name = directory_entry(&from_path, to_path.file_name().unwrap(), &params);
+        from_path.push(name);
         params.from = from_path.into_os_string();
     } else if from_path.is_file() && to_path.is_dir() {
-        to_path.push(from_path.file_name().unwrap());
+        let name = directory_entry(&to_path, from_path.file_name().unwrap(), &params);
+        to_path.push(name);
         params.to = to_path.into_os_string();
     }
 
@@ -378,6 +385,61 @@ pub fn parse_params<I: Iterator<Item = OsString>>(
     Ok((params, options))
 }
 
+/// Returns the name of the entry of `dir` to compare with a file named
+/// `name`: `name` itself, or with --ignore-file-name-case, an entry whose name
+/// differs only by case when `name` does not exist.
+fn directory_entry(dir: &Path, name: &OsStr, params: &Params) -> OsString {
+    if params.ignore_file_name_case && !dir.join(name).exists() {
+        let wanted = fold_file_name_case(name);
+        let entries = std::fs::read_dir(dir).into_iter().flatten().flatten();
+        if let Some(entry) = entries
+            .map(|entry| entry.file_name())
+            .find(|entry| fold_file_name_case(entry) == wanted)
+        {
+            return entry;
+        }
+    }
+    name.to_os_string()
+}
+
+/// How the argument of an option is given.
+enum OptionArgument<'a> {
+    /// In the same command line argument, as in `-Fx` or `--show-function-line=x`.
+    Attached(&'a str),
+    /// As the next command line argument.
+    Separate,
+}
+
+/// Returns how the argument of the option named `short` (like `-F`) or
+/// `long` is given, if `param` is that option.
+fn option_argument<'a>(param: &'a OsStr, short: &str, long: &str) -> Option<OptionArgument<'a>> {
+    if param == short || param == long {
+        return Some(OptionArgument::Separate);
+    }
+    let param = param.to_str()?;
+    param
+        .strip_prefix(long)
+        .and_then(|rest| rest.strip_prefix('='))
+        .or_else(|| param.strip_prefix(short).filter(|value| !value.is_empty()))
+        .map(OptionArgument::Attached)
+}
+
+/// Returns the value of the argument of the option `param`, taking the next
+/// command line argument when it is not attached.
+fn argument_value(
+    argument: OptionArgument,
+    param: &OsStr,
+    opts: &mut impl Iterator<Item = (usize, OsString)>,
+) -> Result<OsString, String> {
+    match argument {
+        OptionArgument::Attached(value) => Ok(value.into()),
+        OptionArgument::Separate => opts
+            .next()
+            .map(|(_, value)| value)
+            .ok_or_else(|| format!("option '{}' requires an argument", param.to_string_lossy())),
+    }
+}
+
 /// Validates and records a `-F` pattern.
 fn push_function_line_pattern(params: &mut Params, pattern: &str) -> Result<(), String> {
     let bre = Bre::new(pattern).map_err(|error| format!("'{pattern}': {error}"))?;
@@ -1208,4 +1270,51 @@ mod tests {
         );
         assert_eq!(options(&["diff", "-", "new", "-t"]), [os("-t")]);
     }
+
+    #[test]
+    fn starting_file() {
+        for args in [
+            &["-S", "mid"][..],
+            &["-Smid"],
+            &["--starting-file=mid"],
+            &["--starting-file", "mid"],
+        ] {
+            let args = std::iter::once("diff")
+                .chain(args.iter().copied())
+                .chain(["foo", "bar"]);
+            let params = parse_params(args.map(os).peekable()).unwrap();
+            assert_eq!(params.starting_file, Some(os("mid")));
+            assert_eq!(params.from, os("foo"));
+        }
+        assert!(parse_params(
+            [os("diff"), os("foo"), os("bar"), os("-S")]
+                .into_iter()
+                .peekable()
+        )
+        .is_err());
+    }
+    #[test]
+    fn ignore_file_name_case() {
+        // The last of --ignore-file-name-case and --no-ignore-file-name-case
+        // wins.
+        for (args, expected) in [
+            (&[][..], false),
+            (&["--ignore-file-name-case"], true),
+            (&["--no-ignore-file-name-case"], false),
+            (
+                &["--ignore-file-name-case", "--no-ignore-file-name-case"],
+                false,
+            ),
+            (
+                &["--no-ignore-file-name-case", "--ignore-file-name-case"],
+                true,
+            ),
+        ] {
+            let args = std::iter::once("diff")
+                .chain(args.iter().copied())
+                .chain(["foo", "bar"]);
+            let params = parse_params(args.map(os).peekable()).unwrap();
+            assert_eq!(params.ignore_file_name_case, expected);
+        }
+    }
 }
diff --git a/src/utils.rs b/src/utils.rs
index 0265109..7247fe9 100644
--- a/src/utils.rs
+++ b/src/utils.rs
@@ -147,6 +147,14 @@ pub fn quote_shell_argument(arg: &[u8]) -> Cow<'_, [u8]> {
     Cow::Owned(quoted)
 }
 
+/// Returns `name` in lowercase, to match file names ignoring case.
+pub fn fold_file_name_case(name: &OsStr) -> Vec<u8> {
+    match name.to_str() {
+        Some(name) => name.to_lowercase().into_bytes(),
+        None => name.as_encoded_bytes().to_ascii_lowercase(),
+    }
+}
+
 /// Finds the lines shown after hunk headers by `-F` and `-p`: the nearest
 /// line of the old file preceding a hunk that matches one of the patterns.
 pub struct FunctionLineFinder<'a> {
diff --git a/tests/by-util/test_diff.rs b/tests/by-util/test_diff.rs
index 2b29278..0292275 100644
--- a/tests/by-util/test_diff.rs
+++ b/tests/by-util/test_diff.rs
@@ -618,6 +618,76 @@ fn compare_directories_special_entries() -> Result<(), Box<dyn std::error::Error
     Ok(())
 }
 
+#[test]
+fn directory_name_matching() -> Result<(), Box<dyn std::error::Error>> {
+    let tmp_dir = tempdir()?;
+    let left = tmp_dir.path().join("left");
+    let right = tmp_dir.path().join("right");
+    std::fs::create_dir_all(left.join("lib"))?;
+    std::fs::create_dir_all(right.join("lib"))?;
+    for name in ["Readme", "notes", "lib/early"] {
+        std::fs::write(left.join(name), "v1\n")?;
+    }
+    for name in ["readme", "Notes", "Todo", "lib/EARLY"] {
+        std::fs::write(right.join(name), "v1\n")?;
+    }
+    // Names differing only by case can only coexist on case-sensitive file
+    // systems; there, they pair in byte order.
+    std::fs::write(left.join("README"), "v1\n")?;
+    let case_sensitive = std::fs::read_dir(&left)?.count() == 4;
+    let unpaired_readme = if case_sensitive {
+        format!("Only in {}: Readme\n", left.display())
+    } else {
+        String::new()
+    };
+    let left = left.to_str().unwrap();
+    let right = right.to_str().unwrap();
+    let s = std::path::MAIN_SEPARATOR;
+
+    let mut cmd = cargo_bin_cmd!("diffutils");
+    cmd.arg("diff")
+        .arg("-r")
+        .arg("--ignore-file-name-case")
+        .arg(left)
+        .arg(right);
+    cmd.assert()
+        .code(predicate::eq(1))
+        .stdout(format!("{unpaired_readme}Only in {right}: Todo\n"));
+
+    // -S only skips names at the top level.
+    let mut cmd = cargo_bin_cmd!("diffutils");
+    cmd.arg("diff")
+        .arg("-r")
+        .arg("-S")
+        .arg("l")
+        .arg(left)
+        .arg(right);
+    cmd.assert().code(predicate::eq(1)).stdout(format!(
+        "Only in {right}{s}lib: EARLY\nOnly in {left}{s}lib: early\n\
+         Only in {left}: notes\nOnly in {right}: readme\n"
+    ));
+
+    // The starting name is matched regardless of case too.
+    let mut cmd = cargo_bin_cmd!("diffutils");
+    cmd.arg("diff")
+        .arg("--starting-file=NOTES")
+        .arg("--ignore-file-name-case")
+        .arg(left)
+        .arg(right);
+    cmd.assert()
+        .code(predicate::eq(1))
+        .stdout(format!("{unpaired_readme}Only in {right}: Todo\n"));
+
+    // A file compared with a directory finds its counterpart regardless of case.
+    let mut cmd = cargo_bin_cmd!("diffutils");
+    cmd.arg("diff")
+        .arg("--ignore-file-name-case")
+        .arg(format!("{left}{s}notes"))
+        .arg(right);
+    cmd.assert().code(predicate::eq(0)).stdout("");
+    Ok(())
+}
+
 #[test]
 fn compare_file_to_directory() -> Result<(), Box<dyn std::error::Error>> {
     let tmp_dir = tempdir()?;