diff --git a/lib/compress.js b/lib/compress.js
index 202ce8f1d8b..d5057db5421 100644
--- a/lib/compress.js
+++ b/lib/compress.js
@@ -6317,7 +6317,7 @@ Compressor.prototype.compress = function(node) {
             if (typeof this.key != "string") return false;
             var value = this.value;
             if (!value) return true;
-            return walk_scoped(value, scope);
+            return this.static ? value.is_constant_expression(scope) : walk_scoped(value, scope);
         });
         def(AST_Constant, return_true);
         def(AST_Lambda, function(scope) {
@@ -6326,6 +6326,9 @@ Compressor.prototype.compress = function(node) {
         def(AST_Object, function(scope) {
             return all_constant(this.properties, scope);
         });
+        def(AST_ObjectIdentity, function(scope) {
+            return this.scope.resolve() === scope;
+        });
         def(AST_ObjectProperty, function(scope) {
             return typeof this.key == "string" && this.value.is_constant_expression(scope);
         });
diff --git a/test/compress/classes.js b/test/compress/classes.js
index 0e1e0217167..4335809bb63 100644
--- a/test/compress/classes.js
+++ b/test/compress/classes.js
@@ -3196,7 +3196,7 @@ issue_5082_2: {
     node_version: ">=12"
 }
 
-issue_5082_2_static: {
+issue_5082_2_strict: {
     options = {
         inline: true,
         passes: 2,
@@ -4059,3 +4059,56 @@ issue_5874: {
     expect_stdout: "PASS"
     node_version: ">=12"
 }
+
+issue_5876_1: {
+    options = {
+        reduce_vars: true,
+        toplevel: true,
+        unused: true,
+    }
+    input: {
+        class A {
+            static p = this.q;
+            f() {}
+        }
+        if (A)
+            console.log("PASS");
+    }
+    expect: {
+        class A {
+            static p = this.q;
+            f() {}
+        }
+        if (A)
+            console.log("PASS");
+    }
+    expect_stdout: "PASS"
+    node_version: ">=12"
+}
+
+issue_5876_2: {
+    options = {
+        reduce_vars: true,
+        toplevel: true,
+        unused: true,
+    }
+    input: {
+        class A {
+            static p = console.log("foo");
+        }
+        if (A)
+            console.log("bar");
+    }
+    expect: {
+        class A {
+            static p = console.log("foo");
+        }
+        if (A)
+            console.log("bar");
+    }
+    expect_stdout: [
+        "foo",
+        "bar",
+    ]
+    node_version: ">=12"
+}
diff --git a/test/compress/functions.js b/test/compress/functions.js
index 04c42031f30..2fa172fcf8f 100644
--- a/test/compress/functions.js
+++ b/test/compress/functions.js
@@ -8242,9 +8242,7 @@ issue_5328: {
         })(this);
     }
     expect: {
-        (function(arguments) {
-            console.log(Object.keys(arguments).join());
-        })(this);
+        void console.log(Object.keys(this).join());
     }
     expect_stdout: ""
 }
diff --git a/test/compress/reduce_vars.js b/test/compress/reduce_vars.js
index 7b7cb67066d..36deccf0bcb 100644
--- a/test/compress/reduce_vars.js
+++ b/test/compress/reduce_vars.js
@@ -6882,9 +6882,7 @@ issue_3622: {
     }
     expect: {
         var c = "FAIL";
-        var a;
-        a = this,
-        !void (a && (c = "PASS")),
+        !void (this && (c = "PASS")),
         console.log(c);
     }
     expect_stdout: "PASS"