diff --git a/apps/p4-tutorial/pipeconf/src/main/java/org/onosproject/p4tutorial/pipeconf/PipelineInterpreterImpl.java b/apps/p4-tutorial/pipeconf/src/main/java/org/onosproject/p4tutorial/pipeconf/PipelineInterpreterImpl.java
index fd3b504..828d623 100644
--- a/apps/p4-tutorial/pipeconf/src/main/java/org/onosproject/p4tutorial/pipeconf/PipelineInterpreterImpl.java
+++ b/apps/p4-tutorial/pipeconf/src/main/java/org/onosproject/p4tutorial/pipeconf/PipelineInterpreterImpl.java
@@ -16,9 +16,8 @@
 
 package org.onosproject.p4tutorial.pipeconf;
 
-import com.google.common.collect.BiMap;
-import com.google.common.collect.ImmutableBiMap;
 import com.google.common.collect.ImmutableList;
+import com.google.common.collect.ImmutableMap;
 import com.google.common.collect.Lists;
 import org.onlab.packet.DeserializationException;
 import org.onlab.packet.Ethernet;
@@ -50,6 +49,7 @@
 import java.nio.ByteBuffer;
 import java.util.Collection;
 import java.util.List;
+import java.util.Map;
 import java.util.Optional;
 
 import static java.lang.String.format;
@@ -98,13 +98,13 @@
     private static final PiActionParamId ACT_PARAM_ID_PORT =
             PiActionParamId.of("port");
 
-    private static final BiMap<Integer, PiTableId> TABLE_MAP =
-            new ImmutableBiMap.Builder<Integer, PiTableId>()
+    private static final Map<Integer, PiTableId> TABLE_MAP =
+            new ImmutableMap.Builder<Integer, PiTableId>()
                     .put(0, TABLE_L2_FWD_ID)
                     .build();
 
-    private static final BiMap<Criterion.Type, PiMatchFieldId> CRITERION_MAP =
-            new ImmutableBiMap.Builder<Criterion.Type, PiMatchFieldId>()
+    private static final Map<Criterion.Type, PiMatchFieldId> CRITERION_MAP =
+            ImmutableMap.<Criterion.Type, PiMatchFieldId>builder()
                     .put(Criterion.Type.IN_PORT, INGRESS_PORT_ID)
                     .put(Criterion.Type.ETH_DST, ETH_DST_ID)
                     .put(Criterion.Type.ETH_SRC, ETH_SRC_ID)
@@ -117,21 +117,11 @@
     }
 
     @Override
-    public Optional<Criterion.Type> mapPiMatchFieldId(PiMatchFieldId headerFieldId) {
-        return Optional.ofNullable(CRITERION_MAP.inverse().get(headerFieldId));
-    }
-
-    @Override
     public Optional<PiTableId> mapFlowRuleTableId(int flowRuleTableId) {
         return Optional.ofNullable(TABLE_MAP.get(flowRuleTableId));
     }
 
     @Override
-    public Optional<Integer> mapPiTableId(PiTableId piTableId) {
-        return Optional.ofNullable(TABLE_MAP.inverse().get(piTableId));
-    }
-
-    @Override
     public PiAction mapTreatment(TrafficTreatment treatment, PiTableId piTableId)
             throws PiInterpreterException {
 
diff --git a/core/api/src/main/java/org/onosproject/net/pi/model/PiPipelineInterpreter.java b/core/api/src/main/java/org/onosproject/net/pi/model/PiPipelineInterpreter.java
index 1d1301e..1ba85e0 100644
--- a/core/api/src/main/java/org/onosproject/net/pi/model/PiPipelineInterpreter.java
+++ b/core/api/src/main/java/org/onosproject/net/pi/model/PiPipelineInterpreter.java
@@ -47,16 +47,6 @@
     Optional<PiMatchFieldId> mapCriterionType(Criterion.Type type);
 
     /**
-     * Returns the criterion type that is equivalent to the given PI match field
-     * ID, if present. If not present, it means that the given match field is
-     * not supported by this interpreter.
-     *
-     * @param fieldId match field ID
-     * @return optional criterion type
-     */
-    Optional<Criterion.Type> mapPiMatchFieldId(PiMatchFieldId fieldId);
-
-    /**
      * Returns a PI table ID equivalent to the given numeric table ID (as in
      * {@link org.onosproject.net.flow.FlowRule#tableId()}). If not present, it
      * means that the given integer table ID cannot be mapped to any table of
@@ -72,18 +62,6 @@
     Optional<PiTableId> mapFlowRuleTableId(int flowRuleTableId);
 
     /**
-     * Returns an integer table ID equivalent to the given PI table ID. If not
-     * present, it means that the given PI table ID cannot be mapped to any
-     * integer table ID, because such mapping would be meaningless or because
-     * such PI table ID is not defined by the pipeline model.
-     *
-     * @param piTableId PI table ID
-     * @return numeric table ID
-     */
-    // FIXME: as above
-    Optional<Integer> mapPiTableId(PiTableId piTableId);
-
-    /**
      * Returns an action of a PI pipeline that is functionally equivalent to the
      * given traffic treatment for the given table.
      *
diff --git a/core/net/src/main/java/org/onosproject/net/pi/impl/PiFlowRuleTranslatorImpl.java b/core/net/src/main/java/org/onosproject/net/pi/impl/PiFlowRuleTranslatorImpl.java
index e910116..561d62a 100644
--- a/core/net/src/main/java/org/onosproject/net/pi/impl/PiFlowRuleTranslatorImpl.java
+++ b/core/net/src/main/java/org/onosproject/net/pi/impl/PiFlowRuleTranslatorImpl.java
@@ -54,7 +54,6 @@
 
 import java.util.Collection;
 import java.util.Map;
-import java.util.Optional;
 import java.util.Set;
 import java.util.StringJoiner;
 
@@ -80,7 +79,8 @@
     }
 
     /**
-     * Returns a PI table entry equivalent to the given flow rule, for the given pipeconf and device.
+     * Returns a PI table entry equivalent to the given flow rule, for the given
+     * pipeconf and device.
      *
      * @param rule     flow rule
      * @param pipeconf pipeconf
@@ -148,7 +148,7 @@
                 tableEntryBuilder.withTimeout((double) rule.timeout());
             } else {
                 log.debug("Flow rule is temporary, but table '{}' doesn't support " +
-                                 "aging, translating to permanent.", tableModel.id());
+                                  "aging, translating to permanent.", tableModel.id());
             }
 
         }
@@ -158,16 +158,19 @@
 
 
     /**
-     * Returns a PI action equivalent to the given treatment, optionally using the given interpreter. This method also
-     * checks that the produced PI table action is suitable for the given table ID and pipeline model. If suitable, the
-     * returned action instance will have parameters well-sized, according to the table model.
+     * Returns a PI action equivalent to the given treatment, optionally using
+     * the given interpreter. This method also checks that the produced PI table
+     * action is suitable for the given table ID and pipeline model. If
+     * suitable, the returned action instance will have parameters well-sized,
+     * according to the table model.
      *
      * @param treatment     traffic treatment
      * @param interpreter   interpreter
      * @param tableId       PI table ID
      * @param pipelineModel pipeline model
      * @return PI table action
-     * @throws PiTranslationException if the treatment cannot be translated or if the PI action is not suitable for the
+     * @throws PiTranslationException if the treatment cannot be translated or
+     *                                if the PI action is not suitable for the
      *                                given pipeline model
      */
     static PiTableAction translateTreatment(TrafficTreatment treatment, PiPipelineInterpreter interpreter,
@@ -185,7 +188,8 @@
     }
 
     /**
-     * Builds a PI action out of the given treatment, optionally using the given interpreter.
+     * Builds a PI action out of the given treatment, optionally using the given
+     * interpreter.
      */
     private static PiTableAction buildAction(TrafficTreatment treatment, PiPipelineInterpreter interpreter,
                                              PiTableId tableId)
@@ -285,8 +289,9 @@
     }
 
     /**
-     * Builds a collection of PI field matches out of the given selector, optionally using the given interpreter. The
-     * field matches returned are guaranteed to be compatible for the given table model.
+     * Builds a collection of PI field matches out of the given selector,
+     * optionally using the given interpreter. The field matches returned are
+     * guaranteed to be compatible for the given table model.
      */
     private static Collection<PiFieldMatch> translateFieldMatches(PiPipelineInterpreter interpreter,
                                                                   TrafficSelector selector, PiTableModel tableModel)
@@ -312,18 +317,41 @@
         Set<PiMatchFieldId> usedPiCriterionFields = Sets.newHashSet();
         Set<PiMatchFieldId> ignoredPiCriterionFields = Sets.newHashSet();
 
+
+        Map<PiMatchFieldId, Criterion> criterionMap = Maps.newHashMap();
+        if (interpreter != null) {
+            // NOTE: if two criterion types map to the same match field ID, and
+            //  those two criterion types are present in the selector, this won't
+            //  work. This is unlikely to happen since those cases should be
+            //  mutually exclusive:
+            //  e.g. ICMPV6_TYPE ->  metadata.my_normalized_icmp_type
+            //       ICMPV4_TYPE ->  metadata.my_normalized_icmp_type
+            //  A packet can be either ICMPv6 or ICMPv4 but not both.
+            selector.criteria()
+                    .stream()
+                    .map(Criterion::type)
+                    .filter(t -> t != PROTOCOL_INDEPENDENT)
+                    .forEach(t -> {
+                        PiMatchFieldId mfid = interpreter.mapCriterionType(t)
+                                .orElse(null);
+                        if (mfid != null) {
+                            if (criterionMap.containsKey(mfid)) {
+                                log.warn("Detected criterion mapping " +
+                                                 "conflict for PiMatchFieldId {}",
+                                         mfid);
+                            }
+                            criterionMap.put(mfid, selector.getCriterion(t));
+                        }
+                    });
+        }
+
         for (PiMatchFieldModel fieldModel : tableModel.matchFields()) {
 
             PiMatchFieldId fieldId = fieldModel.id();
 
             int bitWidth = fieldModel.bitWidth();
 
-            Optional<Criterion.Type> criterionType =
-                    interpreter == null
-                            ? Optional.empty()
-                            : interpreter.mapPiMatchFieldId(fieldId);
-
-            Criterion criterion = criterionType.map(selector::getCriterion).orElse(null);
+            Criterion criterion = criterionMap.get(fieldId);
 
             if (!piCriterionFields.containsKey(fieldId) && criterion == null) {
                 // Neither a field in PiCriterion is available nor a Criterion mapping is possible.
diff --git a/pipelines/basic/src/main/java/org/onosproject/pipelines/basic/BasicInterpreterImpl.java b/pipelines/basic/src/main/java/org/onosproject/pipelines/basic/BasicInterpreterImpl.java
index fe3c22f..6e05a5b 100644
--- a/pipelines/basic/src/main/java/org/onosproject/pipelines/basic/BasicInterpreterImpl.java
+++ b/pipelines/basic/src/main/java/org/onosproject/pipelines/basic/BasicInterpreterImpl.java
@@ -16,8 +16,8 @@
 
 package org.onosproject.pipelines.basic;
 
-import com.google.common.collect.ImmutableBiMap;
 import com.google.common.collect.ImmutableList;
+import com.google.common.collect.ImmutableMap;
 import org.onlab.packet.DeserializationException;
 import org.onlab.packet.Ethernet;
 import org.onlab.util.ImmutableByteSequence;
@@ -45,6 +45,7 @@
 import java.nio.ByteBuffer;
 import java.util.Collection;
 import java.util.List;
+import java.util.Map;
 import java.util.Optional;
 
 import static java.lang.String.format;
@@ -80,12 +81,12 @@
 
     private static final int PORT_BITWIDTH = 9;
 
-    private static final ImmutableBiMap<Integer, PiTableId> TABLE_MAP =
-            new ImmutableBiMap.Builder<Integer, PiTableId>()
+    private static final Map<Integer, PiTableId> TABLE_MAP =
+            new ImmutableMap.Builder<Integer, PiTableId>()
                     .put(0, BasicConstants.INGRESS_TABLE0_CONTROL_TABLE0)
                     .build();
-    private static final ImmutableBiMap<Criterion.Type, PiMatchFieldId> CRITERION_MAP =
-            new ImmutableBiMap.Builder<Criterion.Type, PiMatchFieldId>()
+    private static final Map<Criterion.Type, PiMatchFieldId> CRITERION_MAP =
+            new ImmutableMap.Builder<Criterion.Type, PiMatchFieldId>()
                     .put(Criterion.Type.IN_PORT, HDR_STANDARD_METADATA_INGRESS_PORT)
                     .put(Criterion.Type.ETH_DST, HDR_HDR_ETHERNET_DST_ADDR)
                     .put(Criterion.Type.ETH_SRC, HDR_HDR_ETHERNET_SRC_ADDR)
@@ -236,17 +237,7 @@
     }
 
     @Override
-    public Optional<Criterion.Type> mapPiMatchFieldId(PiMatchFieldId headerFieldId) {
-        return Optional.ofNullable(CRITERION_MAP.inverse().get(headerFieldId));
-    }
-
-    @Override
     public Optional<PiTableId> mapFlowRuleTableId(int flowRuleTableId) {
         return Optional.ofNullable(TABLE_MAP.get(flowRuleTableId));
     }
-
-    @Override
-    public Optional<Integer> mapPiTableId(PiTableId piTableId) {
-        return Optional.ofNullable(TABLE_MAP.inverse().get(piTableId));
-    }
 }
diff --git a/pipelines/fabric/src/main/java/org/onosproject/pipelines/fabric/FabricInterpreter.java b/pipelines/fabric/src/main/java/org/onosproject/pipelines/fabric/FabricInterpreter.java
index e523472..dcd872b 100644
--- a/pipelines/fabric/src/main/java/org/onosproject/pipelines/fabric/FabricInterpreter.java
+++ b/pipelines/fabric/src/main/java/org/onosproject/pipelines/fabric/FabricInterpreter.java
@@ -99,25 +99,6 @@
                     .put(Criterion.Type.ICMPV6_CODE, FabricConstants.HDR_ICMP_CODE)
                     .build();
 
-    private static final ImmutableMap<PiMatchFieldId, Criterion.Type> INVERSE_CRITERION_MAP =
-            ImmutableMap.<PiMatchFieldId, Criterion.Type>builder()
-                    .put(FabricConstants.HDR_IG_PORT, Criterion.Type.IN_PORT)
-                    .put(FabricConstants.HDR_ETH_DST, Criterion.Type.ETH_DST_MASKED)
-                    .put(FabricConstants.HDR_ETH_SRC, Criterion.Type.ETH_SRC_MASKED)
-                    .put(FabricConstants.HDR_ETH_TYPE, Criterion.Type.ETH_TYPE)
-                    .put(FabricConstants.HDR_MPLS_LABEL, Criterion.Type.MPLS_LABEL)
-                    .put(FabricConstants.HDR_VLAN_ID, Criterion.Type.VLAN_VID)
-                    .put(FabricConstants.HDR_IPV4_DST, Criterion.Type.IPV4_DST)
-                    .put(FabricConstants.HDR_IPV4_SRC, Criterion.Type.IPV4_SRC)
-                    .put(FabricConstants.HDR_IPV6_DST, Criterion.Type.IPV6_DST)
-                    // FIXME: might be incorrect if we inverse the map....
-                    .put(FabricConstants.HDR_L4_SPORT, Criterion.Type.UDP_SRC)
-                    .put(FabricConstants.HDR_L4_DPORT, Criterion.Type.UDP_DST)
-                    .put(FabricConstants.HDR_IP_PROTO, Criterion.Type.IP_PROTO)
-                    .put(FabricConstants.HDR_ICMP_TYPE, Criterion.Type.ICMPV6_TYPE)
-                    .put(FabricConstants.HDR_ICMP_CODE, Criterion.Type.ICMPV6_CODE)
-                    .build();
-
     private static final PiAction NOP = PiAction.builder()
             .withId(FabricConstants.NOP).build();
 
@@ -132,11 +113,6 @@
     }
 
     @Override
-    public Optional<Criterion.Type> mapPiMatchFieldId(PiMatchFieldId fieldId) {
-        return Optional.ofNullable(INVERSE_CRITERION_MAP.get(fieldId));
-    }
-
-    @Override
     public Optional<PiTableId> mapFlowRuleTableId(int flowRuleTableId) {
         // The only use case for Index ID->PiTableId is when using the single
         // table pipeliner. fabric.p4 is never used with such pipeliner.
@@ -144,13 +120,6 @@
     }
 
     @Override
-    public Optional<Integer> mapPiTableId(PiTableId piTableId) {
-        // The only use case for Index ID->PiTableId is when using the single
-        // table pipeliner. fabric.p4 is never used with such pipeliner.
-        return Optional.empty();
-    }
-
-    @Override
     public PiAction mapTreatment(TrafficTreatment treatment, PiTableId piTableId)
             throws PiInterpreterException {
         if (FILTERING_CTRL_TBLS.contains(piTableId)) {