diff --git a/src/Monolog/Handler/Handler.php b/src/Monolog/Handler/Handler.php
index 1af68b66..27e48abd 100644
--- a/src/Monolog/Handler/Handler.php
+++ b/src/Monolog/Handler/Handler.php
@@ -39,7 +39,7 @@ abstract class Handler implements HandlerInterface
     {
         try {
             $this->close();
-        } catch (\Exception $e) {
+        } catch (\Throwable $e) {
             // do nothing
         }
     }
diff --git a/src/Monolog/Handler/WhatFailureGroupHandler.php b/src/Monolog/Handler/WhatFailureGroupHandler.php
index db793869..953fdc07 100644
--- a/src/Monolog/Handler/WhatFailureGroupHandler.php
+++ b/src/Monolog/Handler/WhatFailureGroupHandler.php
@@ -33,7 +33,7 @@ class WhatFailureGroupHandler extends GroupHandler
         foreach ($this->handlers as $handler) {
             try {
                 $handler->handle($record);
-            } catch (\Exception $e) {
+            } catch (\Throwable $e) {
                 // What failure?
             } catch (\Throwable $e) {
                 // What failure?
@@ -51,7 +51,7 @@ class WhatFailureGroupHandler extends GroupHandler
         foreach ($this->handlers as $handler) {
             try {
                 $handler->handleBatch($records);
-            } catch (\Exception $e) {
+            } catch (\Throwable $e) {
                 // What failure?
             } catch (\Throwable $e) {
                 // What failure?