diff --git a/core/src/main/java/io/grpc/internal/LogExceptionRunnable.java b/core/src/main/java/io/grpc/internal/LogExceptionRunnable.java
index 359a35f9c5..2b0e5b2a05 100644
--- a/core/src/main/java/io/grpc/internal/LogExceptionRunnable.java
+++ b/core/src/main/java/io/grpc/internal/LogExceptionRunnable.java
@@ -33,6 +33,8 @@ package io.grpc.internal;
 
 import static com.google.common.base.Preconditions.checkNotNull;
 
+import com.google.common.base.Throwables;
+
 import java.util.logging.Level;
 import java.util.logging.Logger;
 
@@ -56,7 +58,8 @@ public final class LogExceptionRunnable implements Runnable {
       task.run();
     } catch (Throwable t) {
       log.log(Level.SEVERE, "Exception while executing runnable " + task, t);
-      throw t instanceof RuntimeException ? (RuntimeException) t : new RuntimeException(t);
+      Throwables.propagateIfPossible(t);
+      throw new AssertionError(t);
     }
   }
 
diff --git a/core/src/main/java/io/grpc/internal/ServerImpl.java b/core/src/main/java/io/grpc/internal/ServerImpl.java
index a4a40cb9ba..08777309b7 100644
--- a/core/src/main/java/io/grpc/internal/ServerImpl.java
+++ b/core/src/main/java/io/grpc/internal/ServerImpl.java
@@ -364,10 +364,10 @@ public final class ServerImpl extends io.grpc.Server {
               stream.close(Status.fromThrowable(e), new Metadata());
               context.cancel(null);
               throw e;
-            } catch (Throwable t) {
-              stream.close(Status.fromThrowable(t), new Metadata());
+            } catch (Error e) {
+              stream.close(Status.fromThrowable(e), new Metadata());
               context.cancel(null);
-              throw new RuntimeException(t);
+              throw e;
             } finally {
               jumpListener.setListener(listener);
             }
@@ -487,9 +487,9 @@ public final class ServerImpl extends io.grpc.Server {
           } catch (RuntimeException e) {
             internalClose(Status.fromThrowable(e), new Metadata());
             throw e;
-          } catch (Throwable t) {
-            internalClose(Status.fromThrowable(t), new Metadata());
-            throw new RuntimeException(t);
+          } catch (Error e) {
+            internalClose(Status.fromThrowable(e), new Metadata());
+            throw e;
           }
         }
       });
@@ -505,9 +505,9 @@ public final class ServerImpl extends io.grpc.Server {
           } catch (RuntimeException e) {
             internalClose(Status.fromThrowable(e), new Metadata());
             throw e;
-          } catch (Throwable t) {
-            internalClose(Status.fromThrowable(t), new Metadata());
-            throw new RuntimeException(t);
+          } catch (Error e) {
+            internalClose(Status.fromThrowable(e), new Metadata());
+            throw e;
           }
         }
       });