diff --git a/src/diagnostics/rules/redundant_readme.rs b/src/diagnostics/rules/redundant_readme.rs
index 9df1ae1134c..c7897286d5c 100644
--- a/src/diagnostics/rules/redundant_readme.rs
+++ b/src/diagnostics/rules/redundant_readme.rs
@@ -22,6 +22,7 @@ use crate::diagnostics::workspace_rel_path;
 use crate::workspace::Package;
 use crate::workspace::Workspace;
 use crate::workspace::parser::DEFAULT_README_FILES;
+use crate::workspace::parser::default_readme_from_package_root;
 
 pub static LINT: &Lint = &Lint {
     name: "redundant_readme",
@@ -109,7 +110,9 @@ fn lint_package_inner(
         return Ok(());
     };
 
-    if !DEFAULT_README_FILES.contains(&readme.as_str()) {
+    if !DEFAULT_README_FILES.contains(&readme.as_str())
+        || default_readme_from_package_root(pkg.root()).as_deref() != Some(readme)
+    {
         return Ok(());
     }
 
diff --git a/src/workspace/parser/mod.rs b/src/workspace/parser/mod.rs
index 4098ef06dd0..e86bd4e95c6 100644
--- a/src/workspace/parser/mod.rs
+++ b/src/workspace/parser/mod.rs
@@ -859,7 +859,7 @@ pub const DEFAULT_README_FILES: [&str; 3] = ["README.md", "README.txt", "README"
 
 /// Checks if a file with any of the default README file names exists in the package root.
 /// If so, returns a `String` representing that name.
-fn default_readme_from_package_root(package_root: &Path) -> Option<String> {
+pub(crate) fn default_readme_from_package_root(package_root: &Path) -> Option<String> {
     for &readme_filename in DEFAULT_README_FILES.iter() {
         if package_root.join(readme_filename).is_file() {
             return Some(readme_filename.to_string());
diff --git a/tests/testsuite/lints/redundant_readme.rs b/tests/testsuite/lints/redundant_readme.rs
index 5a0865caaa5..c820a9a91bc 100644
--- a/tests/testsuite/lints/redundant_readme.rs
+++ b/tests/testsuite/lints/redundant_readme.rs
@@ -41,6 +41,74 @@ redundant_readme = "warn"
         .run();
 }
 
+#[cargo_test]
+fn lower_priority_readme() {
+    let p = project()
+        .file(
+            "Cargo.toml",
+            r#"
+[package]
+name = "foo"
+version = "0.0.1"
+edition = "2015"
+authors = []
+readme = "README.txt"
+
+[lints.cargo]
+default = { level = "allow", priority = -1 }
+redundant_readme = "warn"
+"#,
+        )
+        .file("src/main.rs", "fn main() {}")
+        .file("README.md", "")
+        .file("README.txt", "")
+        .build();
+
+    p.cargo("fetch -Zcargo-lints")
+        .masquerade_as_nightly_cargo(&["cargo-lints"])
+        .with_stderr_data(str![""])
+        .run();
+}
+
+#[cargo_test]
+fn explicit_readme_txt() {
+    let p = project()
+        .file(
+            "Cargo.toml",
+            r#"
+[package]
+name = "foo"
+version = "0.0.1"
+edition = "2015"
+authors = []
+readme = "README.txt"
+
+[lints.cargo]
+default = { level = "allow", priority = -1 }
+redundant_readme = "warn"
+"#,
+        )
+        .file("src/main.rs", "fn main() {}")
+        .file("README.txt", "")
+        .build();
+
+    p.cargo("fetch -Zcargo-lints")
+        .masquerade_as_nightly_cargo(&["cargo-lints"])
+        .with_stderr_data(str![[r#"
+[WARNING] explicit `package.readme` can be inferred
+ --> Cargo.toml:7:1
+  |
+7 | readme = "README.txt"
+  | ^^^^^^^^^^^^^^^^^^^^^
+  |
+  = [NOTE] `cargo::redundant_readme` is set to `warn` in `[lints]`
+[HELP] consider removing `package.readme`
+[WARNING] `foo` (manifest) generated 1 warning
+
+"#]])
+        .run();
+}
+
 #[cargo_test]
 fn implicit_readme() {
     let p = project()