diff --git a/config/import-control.xml b/config/import-control.xml
index 1b77f152d..accd8627a 100644
--- a/config/import-control.xml
+++ b/config/import-control.xml
@@ -24,6 +24,7 @@
 
   <!-- The local ones -->
   <allow class="java.security.MessageDigest" local-only="true"/>
+  <allow class="java.security.NoSuchAlgorithmException" local-only="true"/>
   <allow pkg="com.puppycrawl.tools.checkstyle.grammars" local-only="true"/>
   <allow pkg="org.apache.commons.cli" local-only="true"/>
 
diff --git a/config/pmd.xml b/config/pmd.xml
index 6043cf083..72d55e18a 100644
--- a/config/pmd.xml
+++ b/config/pmd.xml
@@ -223,11 +223,15 @@
     <exclude name="UseStringBufferForStringAppends"/>
   </rule>
   <rule ref="rulesets/java/strictexception.xml">
-    <!-- till #959 -->
-    <exclude name="AvoidCatchingGenericException"/>
     <!-- till #961 -->
     <exclude name="AvoidThrowingRawExceptionTypes"/>
   </rule>
+  <rule ref="rulesets/java/strictexception.xml/AvoidCatchingGenericException">
+    <properties>
+        <!-- till #1244 and #1245 -->
+      <property name="violationSuppressXPath" value="//ClassOrInterfaceDeclaration[@Image='Checker' or @Image='CheckstyleAntTask']"/>
+    </properties>
+  </rule>
   <rule ref="rulesets/java/strictexception.xml/ExceptionAsFlowControl">
     <properties>
       <!-- till #1159 -->
diff --git a/src/main/java/com/puppycrawl/tools/checkstyle/PropertyCacheFile.java b/src/main/java/com/puppycrawl/tools/checkstyle/PropertyCacheFile.java
index 81d320359..53b8173ba 100644
--- a/src/main/java/com/puppycrawl/tools/checkstyle/PropertyCacheFile.java
+++ b/src/main/java/com/puppycrawl/tools/checkstyle/PropertyCacheFile.java
@@ -27,6 +27,7 @@ import java.io.ByteArrayOutputStream;
 import java.io.ObjectOutputStream;
 import java.io.OutputStream;
 import java.io.Serializable;
+import java.security.NoSuchAlgorithmException;
 import java.util.Properties;
 import java.security.MessageDigest;
 
@@ -202,9 +203,9 @@ final class PropertyCacheFile {
 
             return hexEncode(md.digest());
         }
-        catch (final Exception ex) { // IO, NoSuchAlgorithm
-            LOG.debug("Unable to calculate hashcode.", ex);
-            return "ALWAYS FRESH: " + System.currentTimeMillis();
+        catch (final IOException | NoSuchAlgorithmException ex) {
+            // rethrow as unchecked exception
+            throw new IllegalStateException("Unable to calculate hashcode.", ex);
         }
     }
 
diff --git a/src/main/java/com/puppycrawl/tools/checkstyle/checks/blocks/RightCurlyCheck.java b/src/main/java/com/puppycrawl/tools/checkstyle/checks/blocks/RightCurlyCheck.java
index 05589450c..6a0601a8d 100644
--- a/src/main/java/com/puppycrawl/tools/checkstyle/checks/blocks/RightCurlyCheck.java
+++ b/src/main/java/com/puppycrawl/tools/checkstyle/checks/blocks/RightCurlyCheck.java
@@ -271,7 +271,7 @@ public class RightCurlyCheck extends AbstractOptionCheck<RightCurlyOption> {
                 nextToken = ast;
                 break;
             default:
-                throw new RuntimeException("Unexpected token type ("
+                throw new IllegalStateException("Unexpected token type ("
                         + Utils.getTokenName(ast.getType()) + ")");
         }
 
diff --git a/src/main/java/com/puppycrawl/tools/checkstyle/checks/imports/CustomImportOrderCheck.java b/src/main/java/com/puppycrawl/tools/checkstyle/checks/imports/CustomImportOrderCheck.java
index dd7c13b41..d83fe0636 100644
--- a/src/main/java/com/puppycrawl/tools/checkstyle/checks/imports/CustomImportOrderCheck.java
+++ b/src/main/java/com/puppycrawl/tools/checkstyle/checks/imports/CustomImportOrderCheck.java
@@ -643,7 +643,7 @@ public class CustomImportOrderCheck extends Check {
             try {
                 samePackageMatchingDepth = Integer.parseInt(rule);
             }
-            catch (Exception e) {
+            catch (NumberFormatException e) {
                 samePackageDomainsRegExp = rule;
             }
             customImportOrderRules.add(SAME_PACKAGE_RULE_GROUP);
diff --git a/src/main/java/com/puppycrawl/tools/checkstyle/checks/javadoc/JavadocUtils.java b/src/main/java/com/puppycrawl/tools/checkstyle/checks/javadoc/JavadocUtils.java
index 0ab6cf798..45494f13a 100644
--- a/src/main/java/com/puppycrawl/tools/checkstyle/checks/javadoc/JavadocUtils.java
+++ b/src/main/java/com/puppycrawl/tools/checkstyle/checks/javadoc/JavadocUtils.java
@@ -77,9 +77,10 @@ public final class JavadocUtils {
                     tempTokenValueToName[tokenValue] = name;
                 }
             }
-            catch (Exception e) {
+            catch (IllegalAccessException ex) {
+                // rethrow as unchecked exception
                 throw new IllegalStateException(
-                    "Failed to instantiate collection of Javadoc tokens", e);
+                    "Failed to instantiate collection of Javadoc tokens", ex);
             }
         }