diff --git a/src/main/java/com/fasterxml/jackson/databind/deser/std/StdValueInstantiator.java b/src/main/java/com/fasterxml/jackson/databind/deser/std/StdValueInstantiator.java
index eb2ddd3763..09630b36ab 100644
--- a/src/main/java/com/fasterxml/jackson/databind/deser/std/StdValueInstantiator.java
+++ b/src/main/java/com/fasterxml/jackson/databind/deser/std/StdValueInstantiator.java
@@ -341,7 +341,7 @@ public Object createFromString(DeserializationContext ctxt, String value) throws
         if (_fromStringCreator != null) {
             try {
                 return _fromStringCreator.call1(value);
-            } catch (Throwable t) {
+            } catch (Exception t) {
                 return ctxt.handleInstantiationProblem(_fromStringCreator.getDeclaringClass(),
                         value, rewrapCtorProblem(ctxt, t));
             }
@@ -357,7 +357,7 @@ public Object createFromInt(DeserializationContext ctxt, int value) throws IOExc
             Object arg = Integer.valueOf(value);
             try {
                 return _fromIntCreator.call1(arg);
-            } catch (Throwable t0) {
+            } catch (Exception t0) {
                 return ctxt.handleInstantiationProblem(_fromIntCreator.getDeclaringClass(),
                         arg, rewrapCtorProblem(ctxt, t0));
             }
@@ -367,7 +367,7 @@ public Object createFromInt(DeserializationContext ctxt, int value) throws IOExc
             Object arg = Long.valueOf(value);
             try {
                 return _fromLongCreator.call1(arg);
-            } catch (Throwable t0) {
+            } catch (Exception t0) {
                 return ctxt.handleInstantiationProblem(_fromLongCreator.getDeclaringClass(),
                         arg, rewrapCtorProblem(ctxt, t0));
             }
@@ -377,7 +377,7 @@ public Object createFromInt(DeserializationContext ctxt, int value) throws IOExc
             Object arg = BigInteger.valueOf(value);
             try {
                 return _fromBigIntegerCreator.call1(arg);
-            } catch (Throwable t0) {
+            } catch (Exception t0) {
                 return ctxt.handleInstantiationProblem(_fromBigIntegerCreator.getDeclaringClass(),
                         arg, rewrapCtorProblem(ctxt, t0)
                 );
@@ -394,7 +394,7 @@ public Object createFromLong(DeserializationContext ctxt, long value) throws IOE
             Long arg = Long.valueOf(value);
             try {
                 return _fromLongCreator.call1(arg);
-            } catch (Throwable t0) {
+            } catch (Exception t0) {
                 return ctxt.handleInstantiationProblem(_fromLongCreator.getDeclaringClass(),
                         arg, rewrapCtorProblem(ctxt, t0)
                 );
@@ -405,7 +405,7 @@ arg, rewrapCtorProblem(ctxt, t0)
             BigInteger arg = BigInteger.valueOf(value);
             try {
                 return _fromBigIntegerCreator.call1(arg);
-            } catch (Throwable t0) {
+            } catch (Exception t0) {
                 return ctxt.handleInstantiationProblem(_fromBigIntegerCreator.getDeclaringClass(),
                         arg, rewrapCtorProblem(ctxt, t0)
                 );
@@ -421,7 +421,7 @@ public Object createFromBigInteger(DeserializationContext ctxt, BigInteger value
         if (_fromBigIntegerCreator != null) {
             try {
                 return _fromBigIntegerCreator.call1(value);
-            } catch (Throwable t) {
+            } catch (Exception t) {
                 return ctxt.handleInstantiationProblem(_fromBigIntegerCreator.getDeclaringClass(),
                         value, rewrapCtorProblem(ctxt, t)
                 );
@@ -438,7 +438,7 @@ public Object createFromDouble(DeserializationContext ctxt, double value) throws
             Double arg = Double.valueOf(value);
             try {
                 return _fromDoubleCreator.call1(arg);
-            } catch (Throwable t0) {
+            } catch (Exception t0) {
                 return ctxt.handleInstantiationProblem(_fromDoubleCreator.getDeclaringClass(),
                         arg, rewrapCtorProblem(ctxt, t0));
             }
@@ -448,7 +448,7 @@ public Object createFromDouble(DeserializationContext ctxt, double value) throws
             BigDecimal arg = BigDecimal.valueOf(value);
             try {
                 return _fromBigDecimalCreator.call1(arg);
-            } catch (Throwable t0) {
+            } catch (Exception t0) {
                 return ctxt.handleInstantiationProblem(_fromBigDecimalCreator.getDeclaringClass(),
                         arg, rewrapCtorProblem(ctxt, t0));
             }
@@ -463,7 +463,7 @@ public Object createFromBigDecimal(DeserializationContext ctxt, BigDecimal value
         if (_fromBigDecimalCreator != null) {
             try {
                 return _fromBigDecimalCreator.call1(value);
-            } catch (Throwable t) {
+            } catch (Exception t) {
                 return ctxt.handleInstantiationProblem(_fromBigDecimalCreator.getDeclaringClass(),
                         value, rewrapCtorProblem(ctxt, t)
                 );
@@ -479,7 +479,7 @@ value, rewrapCtorProblem(ctxt, t)
             if (dbl != null) {
                 try {
                     return _fromDoubleCreator.call1(dbl);
-                } catch (Throwable t0) {
+                } catch (Exception t0) {
                     return ctxt.handleInstantiationProblem(_fromDoubleCreator.getDeclaringClass(),
                             dbl, rewrapCtorProblem(ctxt, t0));
                 }
@@ -507,7 +507,7 @@ public Object createFromBoolean(DeserializationContext ctxt, boolean value) thro
         final Boolean arg = Boolean.valueOf(value);
         try {
             return _fromBooleanCreator.call1(arg);
-        } catch (Throwable t0) {
+        } catch (Exception t0) {
             return ctxt.handleInstantiationProblem(_fromBooleanCreator.getDeclaringClass(),
                     arg, rewrapCtorProblem(ctxt, t0));
         }
@@ -654,7 +654,7 @@ private Object _createUsingDelegate(AnnotatedWithParams delegateCreator,
             }
             // and then try calling with full set of arguments
             return delegateCreator.call(args);
-        } catch (Throwable t) {
+        } catch (Exception t) {
             throw rewrapCtorProblem(ctxt, t);
         }
     }
diff --git a/src/main/java/com/fasterxml/jackson/databind/ext/DOMDeserializer.java b/src/main/java/com/fasterxml/jackson/databind/ext/DOMDeserializer.java
index 48fc6269fe..085785266a 100644
--- a/src/main/java/com/fasterxml/jackson/databind/ext/DOMDeserializer.java
+++ b/src/main/java/com/fasterxml/jackson/databind/ext/DOMDeserializer.java
@@ -35,18 +35,15 @@ public abstract class DOMDeserializer<T> extends FromStringDeserializer<T>
             parserFactory.setFeature(XMLConstants.FEATURE_SECURE_PROCESSING, true);
         } catch(ParserConfigurationException pce) {
             // not much point to do anything; could log but...
-        } catch (Error e) {
-            // 14-Jul-2016, tatu: Not sure how or why, but during code coverage runs
-            //   (via Cobertura) we get `java.lang.AbstractMethodError` so... ignore that too
         }
 
         // [databind#2589] add two more settings just in case
         try {
             parserFactory.setFeature("http://apache.org/xml/features/disallow-doctype-decl", true);
-        } catch (Throwable t) { } // as per previous one, nothing much to do
+        } catch (Exception t) { } // as per previous one, nothing much to do
         try {
             parserFactory.setFeature("http://apache.org/xml/features/nonvalidating/load-external-dtd", false);
-        } catch (Throwable t) { } // as per previous one, nothing much to do
+        } catch (Exception t) { } // as per previous one, nothing much to do
         DEFAULT_PARSER_FACTORY = parserFactory;
     }
 
diff --git a/src/main/java/com/fasterxml/jackson/databind/ext/NioPathDeserializer.java b/src/main/java/com/fasterxml/jackson/databind/ext/NioPathDeserializer.java
index 20e9d5cf12..e74dde8728 100644
--- a/src/main/java/com/fasterxml/jackson/databind/ext/NioPathDeserializer.java
+++ b/src/main/java/com/fasterxml/jackson/databind/ext/NioPathDeserializer.java
@@ -8,6 +8,7 @@
 import java.nio.file.Path;
 import java.nio.file.Paths;
 import java.nio.file.spi.FileSystemProvider;
+import java.util.ServiceConfigurationError;
 import java.util.ServiceLoader;
 
 import com.fasterxml.jackson.core.JsonParser;
@@ -77,11 +78,11 @@ public Path deserialize(JsonParser p, DeserializationContext ctxt) throws IOExce
                     }
                 }
                 return (Path) ctxt.handleInstantiationProblem(handledType(), value, cause);
-            } catch (Throwable e) {
+            } catch (ServiceConfigurationError e) {
                 e.addSuppressed(cause);
                 return (Path) ctxt.handleInstantiationProblem(handledType(), value, e);
             }
-        } catch (Throwable e) {
+        } catch (Exception e) {
             return (Path) ctxt.handleInstantiationProblem(handledType(), value, e);
         }
     }
diff --git a/src/main/java/com/fasterxml/jackson/databind/util/ClassUtil.java b/src/main/java/com/fasterxml/jackson/databind/util/ClassUtil.java
index f46280c7a8..2bd86d13cb 100644
--- a/src/main/java/com/fasterxml/jackson/databind/util/ClassUtil.java
+++ b/src/main/java/com/fasterxml/jackson/databind/util/ClassUtil.java
@@ -1300,10 +1300,10 @@ public static Method[] getClassMethods(Class<?> cls)
             }
             try {
                 return contextClass.getDeclaredMethods(); // Cross fingers
-            } catch (Throwable t) {
+            } catch (Exception t) {
                 return _failGetClassMethods(cls, t);
             }
-        } catch (Throwable t) {
+        } catch (Exception t) {
             return _failGetClassMethods(cls, t);
         }
     }
diff --git a/src/main/java/com/fasterxml/jackson/databind/util/StdDateFormat.java b/src/main/java/com/fasterxml/jackson/databind/util/StdDateFormat.java
index 05d3168839..45391c2b37 100644
--- a/src/main/java/com/fasterxml/jackson/databind/util/StdDateFormat.java
+++ b/src/main/java/com/fasterxml/jackson/databind/util/StdDateFormat.java
@@ -58,7 +58,7 @@ public class StdDateFormat
                     +"(\\.\\d+)?" // optional second fractions
                     +"(Z|[+-]\\d\\d(?:[:]?\\d\\d)?)?" // optional timeoffset/Z
             );
-        } catch (Throwable t) {
+        } catch (Exception t) {
             throw new RuntimeException(t);
         }
         PATTERN_ISO8601 = p;