diff --git a/crates/uv-resolver/src/pubgrub/dependencies.rs b/crates/uv-resolver/src/pubgrub/dependencies.rs
index 441ce4e48..7bb6e083d 100644
--- a/crates/uv-resolver/src/pubgrub/dependencies.rs
+++ b/crates/uv-resolver/src/pubgrub/dependencies.rs
@@ -121,6 +121,7 @@ impl PubGrubDependencies {
 
                     // Merge the package.
                     if let Some(package) = merge_package(entry.0, &package)? {
+                        dependencies.remove(&package);
                         dependencies.insert(package, version);
                     } else {
                         dependencies.insert(package, version);
diff --git a/crates/uv/tests/pip_compile.rs b/crates/uv/tests/pip_compile.rs
index 91be82141..4de554e0c 100644
--- a/crates/uv/tests/pip_compile.rs
+++ b/crates/uv/tests/pip_compile.rs
@@ -3406,3 +3406,66 @@ fn compile_types_pytz() -> Result<()> {
 
     Ok(())
 }
+
+/// Resolve a package from a `requirements.in` file, with a `constraints.txt` file pinning it to
+/// a specific URL.
+#[test]
+fn compile_constraints_compatible_url() -> Result<()> {
+    let context = TestContext::new("3.12");
+    let requirements_in = context.temp_dir.child("requirements.in");
+    requirements_in.write_str("anyio>4")?;
+
+    let constraints_txt = context.temp_dir.child("constraints.txt");
+    constraints_txt.write_str("anyio @ https://files.pythonhosted.org/packages/bf/cd/d6d9bb1dadf73e7af02d18225cbd2c93f8552e13130484f1c8dcfece292b/anyio-4.2.0-py3-none-any.whl")?;
+
+    uv_snapshot!(context.compile()
+            .arg("requirements.in")
+            .arg("--constraint")
+            .arg("constraints.txt"), @r###"
+    success: true
+    exit_code: 0
+    ----- stdout -----
+    # This file was autogenerated by uv v[VERSION] via the following command:
+    #    uv pip compile --cache-dir [CACHE_DIR] --exclude-newer 2023-11-18T12:00:00Z requirements.in --constraint constraints.txt
+    anyio @ https://files.pythonhosted.org/packages/bf/cd/d6d9bb1dadf73e7af02d18225cbd2c93f8552e13130484f1c8dcfece292b/anyio-4.2.0-py3-none-any.whl
+    idna==3.4
+        # via anyio
+    sniffio==1.3.0
+        # via anyio
+
+    ----- stderr -----
+    Resolved 3 packages in [TIME]
+    "###
+    );
+
+    Ok(())
+}
+
+/// Resolve a package from a `requirements.in` file, with a `constraints.txt` file pinning it to
+/// a specific URL with an incompatible version.
+#[test]
+fn compile_constraints_incompatible_url() -> Result<()> {
+    let context = TestContext::new("3.12");
+    let requirements_in = context.temp_dir.child("requirements.in");
+    requirements_in.write_str("anyio<4")?;
+
+    let constraints_txt = context.temp_dir.child("constraints.txt");
+    constraints_txt.write_str("anyio @ https://files.pythonhosted.org/packages/bf/cd/d6d9bb1dadf73e7af02d18225cbd2c93f8552e13130484f1c8dcfece292b/anyio-4.2.0-py3-none-any.whl")?;
+
+    uv_snapshot!(context.compile()
+            .arg("requirements.in")
+            .arg("--constraint")
+            .arg("constraints.txt"), @r###"
+    success: false
+    exit_code: 1
+    ----- stdout -----
+
+    ----- stderr -----
+      × No solution found when resolving dependencies:
+      ╰─▶ Because only anyio>=4 is available and you require anyio<4, we can
+          conclude that the requirements are unsatisfiable.
+    "###
+    );
+
+    Ok(())
+}