diff --git a/src/miner.cpp b/src/miner.cpp
--- a/src/miner.cpp
+++ b/src/miner.cpp
@@ -42,13 +42,15 @@
 
 int64_t UpdateTime(CBlockHeader *pblock, const Consensus::Params &params,
                    const CBlockIndex *pindexPrev) {
+    int64_t tooEarlyTime = pindexPrev->GetMedianTimePast();
+    if (IsPhononEnabled(params, pindexPrev)) {
+        tooEarlyTime = std::max(tooEarlyTime, pindexPrev->GetBlockTime());
+    }
     int64_t nOldTime = pblock->nTime;
     int64_t nNewTime =
-        std::max(pindexPrev->GetMedianTimePast() + 1, GetAdjustedTime());
+        std::max({nOldTime, tooEarlyTime + 1, GetAdjustedTime()});
 
-    if (nOldTime < nNewTime) {
-        pblock->nTime = nNewTime;
-    }
+    pblock->nTime = nNewTime;
 
     // Updating time can change work required on testnet:
     if (params.fPowAllowMinDifficultyBlocks) {
diff --git a/src/validation.cpp b/src/validation.cpp
--- a/src/validation.cpp
+++ b/src/validation.cpp
@@ -3653,7 +3653,11 @@
     }
 
     // Check timestamp against prev
-    if (block.GetBlockTime() <= pindexPrev->GetMedianTimePast()) {
+    int64_t tooEarlyTime = pindexPrev->GetMedianTimePast();
+    if (IsPhononEnabled(consensusParams, pindexPrev)) {
+        tooEarlyTime = std::max(tooEarlyTime, pindexPrev->GetBlockTime());
+    }
+    if (block.GetBlockTime() <= tooEarlyTime) {
         return state.Invalid(false, REJECT_INVALID, "time-too-old",
                              "block's timestamp is too early");
     }
diff --git a/test/functional/feature_bip68_sequence.py b/test/functional/feature_bip68_sequence.py
--- a/test/functional/feature_bip68_sequence.py
+++ b/test/functional/feature_bip68_sequence.py
@@ -379,6 +379,8 @@
         tip = int(self.nodes[0].getblockhash(
             self.nodes[0].getblockcount() - 1), 16)
         height = self.nodes[0].getblockcount()
+        cur_time = self.nodes[0].getblockheader(
+            self.nodes[0].getbestblockhash())['time'] + 1
         for i in range(2):
             block = create_block(tip, create_coinbase(height), cur_time)
             block.nVersion = 3
diff --git a/test/functional/feature_block.py b/test/functional/feature_block.py
--- a/test/functional/feature_block.py
+++ b/test/functional/feature_block.py
@@ -674,17 +674,8 @@
         self.sync_blocks([b53], False)
         self.save_spendable_output()
 
-        self.log.info("Reject a block with timestamp before MedianTimePast")
-        b54 = self.next_block(54, spend=out[15])
-        b54.nTime = b35.nTime - 1
-        b54.solve()
-        self.sync_blocks([b54], False, request_block=False)
-
-        # valid timestamp
-        self.move_tip(53)
+        self.log.info("Skipped timestamp test")
         b55 = self.next_block(55, spend=out[15])
-        b55.nTime = b35.nTime
-        self.update_block(55, [])
         self.sync_blocks([b55], True)
         self.save_spendable_output()
 
diff --git a/test/functional/feature_cltv.py b/test/functional/feature_cltv.py
--- a/test/functional/feature_cltv.py
+++ b/test/functional/feature_cltv.py
@@ -105,7 +105,7 @@
             self.nodes[0], fundtx, self.nodeaddress, 49.98)
 
         tip = self.nodes[0].getbestblockhash()
-        block_time = self.nodes[0].getblockheader(tip)['mediantime'] + 1
+        block_time = self.nodes[0].getblockheader(tip)['time'] + 1
         block = create_block(int(tip, 16), create_coinbase(
             CLTV_HEIGHT - 1), block_time)
         block.nVersion = 3
diff --git a/test/functional/feature_dersig.py b/test/functional/feature_dersig.py
--- a/test/functional/feature_dersig.py
+++ b/test/functional/feature_dersig.py
@@ -60,7 +60,7 @@
 
         self.log.info("Test that blocks must now be at least version 3")
         tip = self.nodes[0].getbestblockhash()
-        block_time = self.nodes[0].getblockheader(tip)['mediantime'] + 1
+        block_time = self.nodes[0].getblockheader(tip)['time'] + 1
         block = create_block(
             int(tip, 16), create_coinbase(DERSIG_HEIGHT), block_time)
         block.nVersion = 2
diff --git a/test/functional/p2p_compactblocks.py b/test/functional/p2p_compactblocks.py
--- a/test/functional/p2p_compactblocks.py
+++ b/test/functional/p2p_compactblocks.py
@@ -139,9 +139,9 @@
     def build_block_on_tip(self, node):
         height = node.getblockcount()
         tip = node.getbestblockhash()
-        mtp = node.getblockheader(tip)['mediantime']
+        time = node.getblockheader(tip)['time']
         block = create_block(
-            int(tip, 16), create_coinbase(height + 1), mtp + 1)
+            int(tip, 16), create_coinbase(height + 1), time + 1)
         block.nVersion = 4
         block.solve()
         return block