diff --git a/clippy_lints/src/redundant_closure_call.rs b/clippy_lints/src/redundant_closure_call.rs
index efdd78a1c92..17a17890be7 100644
--- a/clippy_lints/src/redundant_closure_call.rs
+++ b/clippy_lints/src/redundant_closure_call.rs
@@ -5,7 +5,7 @@ use clippy_utils::sugg::Sugg;
 use rustc_errors::Applicability;
 use rustc_hir as hir;
 use rustc_hir::intravisit::{Visitor as HirVisitor, Visitor};
-use rustc_hir::{intravisit as hir_visit, CoroutineKind, CoroutineSource};
+use rustc_hir::{intravisit as hir_visit, CoroutineKind, CoroutineSource, Node};
 use rustc_lint::{LateContext, LateLintPass};
 use rustc_middle::hir::nested_filter;
 use rustc_middle::lint::in_external_macro;
@@ -176,12 +176,19 @@ impl<'tcx> LateLintPass<'tcx> for RedundantClosureCall {
                             hint = hint.asyncify();
                         }
 
-                        diag.span_suggestion(
-                            full_expr.span,
-                            "try doing something like",
-                            hint.maybe_par(),
-                            applicability,
-                        );
+                        let is_in_fn_call_arg = clippy_utils::get_parent_node(cx.tcx, expr.hir_id)
+                            .map(|x| match x {
+                                Node::Expr(expr) => matches!(expr.kind, hir::ExprKind::Call(_, _)),
+                                _ => false,
+                            })
+                            .unwrap_or(false);
+
+                        // avoid clippy::double_parens
+                        if !is_in_fn_call_arg {
+                            hint = hint.maybe_par()
+                        };
+
+                        diag.span_suggestion(full_expr.span, "try doing something like", hint, applicability);
                     }
                 },
             );
diff --git a/tests/ui/redundant_closure_call_fixable.fixed b/tests/ui/redundant_closure_call_fixable.fixed
index f2cd9862af6..f272d8359a3 100644
--- a/tests/ui/redundant_closure_call_fixable.fixed
+++ b/tests/ui/redundant_closure_call_fixable.fixed
@@ -3,7 +3,6 @@
 #![allow(clippy::redundant_async_block)]
 #![allow(clippy::type_complexity)]
 #![allow(unused)]
-#![allow(clippy::double_parens)]
 
 async fn something() -> u32 {
     21
@@ -87,7 +86,7 @@ fn issue9956() {
 }
 
 async fn issue11357() {
-    (async {}).await;
+    async {}.await;
 }
 
 mod issue11707 {
@@ -96,6 +95,10 @@ mod issue11707 {
     fn spawn_on(fut: impl Future<Output = ()>) {}
 
     fn demo() {
-        spawn_on((async move {}));
+        spawn_on(async move {});
     }
 }
+
+fn avoid_double_parens() {
+    std::convert::identity(13_i32 + 36_i32).leading_zeros();
+}
diff --git a/tests/ui/redundant_closure_call_fixable.rs b/tests/ui/redundant_closure_call_fixable.rs
index efb08c82e3b..f45db8c9cff 100644
--- a/tests/ui/redundant_closure_call_fixable.rs
+++ b/tests/ui/redundant_closure_call_fixable.rs
@@ -3,7 +3,6 @@
 #![allow(clippy::redundant_async_block)]
 #![allow(clippy::type_complexity)]
 #![allow(unused)]
-#![allow(clippy::double_parens)]
 
 async fn something() -> u32 {
     21
@@ -99,3 +98,7 @@ mod issue11707 {
         spawn_on((|| async move {})());
     }
 }
+
+fn avoid_double_parens() {
+    std::convert::identity((|| 13_i32 + 36_i32)()).leading_zeros();
+}
diff --git a/tests/ui/redundant_closure_call_fixable.stderr b/tests/ui/redundant_closure_call_fixable.stderr
index 16d8797c4aa..028d383ad35 100644
--- a/tests/ui/redundant_closure_call_fixable.stderr
+++ b/tests/ui/redundant_closure_call_fixable.stderr
@@ -1,5 +1,5 @@
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:17:13
+  --> $DIR/redundant_closure_call_fixable.rs:16:13
    |
 LL |     let a = (|| 42)();
    |             ^^^^^^^^^ help: try doing something like: `42`
@@ -8,7 +8,7 @@ LL |     let a = (|| 42)();
    = help: to override `-D warnings` add `#[allow(clippy::redundant_closure_call)]`
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:18:13
+  --> $DIR/redundant_closure_call_fixable.rs:17:13
    |
 LL |       let b = (async || {
    |  _____________^
@@ -28,7 +28,7 @@ LL ~     };
    |
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:23:13
+  --> $DIR/redundant_closure_call_fixable.rs:22:13
    |
 LL |       let c = (|| {
    |  _____________^
@@ -48,13 +48,13 @@ LL ~     };
    |
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:28:13
+  --> $DIR/redundant_closure_call_fixable.rs:27:13
    |
 LL |     let d = (async || something().await)();
    |             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ help: try doing something like: `async { something().await }`
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:37:13
+  --> $DIR/redundant_closure_call_fixable.rs:36:13
    |
 LL |             (|| m!())()
    |             ^^^^^^^^^^^ help: try doing something like: `m!()`
@@ -65,7 +65,7 @@ LL |     m2!();
    = note: this error originates in the macro `m2` (in Nightly builds, run with -Z macro-backtrace for more info)
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:32:13
+  --> $DIR/redundant_closure_call_fixable.rs:31:13
    |
 LL |             (|| 0)()
    |             ^^^^^^^^ help: try doing something like: `0`
@@ -76,64 +76,70 @@ LL |     m2!();
    = note: this error originates in the macro `m` which comes from the expansion of the macro `m2` (in Nightly builds, run with -Z macro-backtrace for more info)
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:45:16
+  --> $DIR/redundant_closure_call_fixable.rs:44:16
    |
 LL |     assert_eq!((|| || 43)()(), 42);
    |                ^^^^^^^^^^^^^^ help: try doing something like: `43`
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:54:10
+  --> $DIR/redundant_closure_call_fixable.rs:53:10
    |
 LL |     dbg!((|| 42)());
    |          ^^^^^^^^^ help: try doing something like: `42`
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:57:13
+  --> $DIR/redundant_closure_call_fixable.rs:56:13
    |
 LL |     let a = (|| || || 123)();
    |             ^^^^^^^^^^^^^^^^ help: try doing something like: `(|| || 123)`
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:61:13
+  --> $DIR/redundant_closure_call_fixable.rs:60:13
    |
 LL |     let a = (|| || || || async || 1)()()()()();
    |             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ help: try doing something like: `async { 1 }`
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:70:13
+  --> $DIR/redundant_closure_call_fixable.rs:69:13
    |
 LL |     let a = (|| echo!(|| echo!(|| 1)))()()();
    |             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ help: try doing something like: `1`
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:72:13
+  --> $DIR/redundant_closure_call_fixable.rs:71:13
    |
 LL |     let a = (|| echo!((|| 123)))()();
    |             ^^^^^^^^^^^^^^^^^^^^^^^^ help: try doing something like: `123`
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:85:11
+  --> $DIR/redundant_closure_call_fixable.rs:84:11
    |
 LL |     bar()((|| || 42)()(), 5);
    |           ^^^^^^^^^^^^^^ help: try doing something like: `42`
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:86:9
+  --> $DIR/redundant_closure_call_fixable.rs:85:9
    |
 LL |     foo((|| || 42)()(), 5);
    |         ^^^^^^^^^^^^^^ help: try doing something like: `42`
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:90:5
+  --> $DIR/redundant_closure_call_fixable.rs:89:5
    |
 LL |     (|| async {})().await;
-   |     ^^^^^^^^^^^^^^^ help: try doing something like: `(async {})`
+   |     ^^^^^^^^^^^^^^^ help: try doing something like: `async {}`
 
 error: try not to call a closure in the expression where it is declared
-  --> $DIR/redundant_closure_call_fixable.rs:99:18
+  --> $DIR/redundant_closure_call_fixable.rs:98:18
    |
 LL |         spawn_on((|| async move {})());
-   |                  ^^^^^^^^^^^^^^^^^^^^ help: try doing something like: `(async move {})`
+   |                  ^^^^^^^^^^^^^^^^^^^^ help: try doing something like: `async move {}`
 
-error: aborting due to 16 previous errors
+error: try not to call a closure in the expression where it is declared
+  --> $DIR/redundant_closure_call_fixable.rs:103:28
+   |
+LL |     std::convert::identity((|| 13_i32 + 36_i32)()).leading_zeros();
+   |                            ^^^^^^^^^^^^^^^^^^^^^^ help: try doing something like: `13_i32 + 36_i32`
+
+error: aborting due to 17 previous errors