diff --git a/changelog.d/gbt-mintime.md b/changelog.d/gbt-mintime.md
new file mode 100644
index 0000000000..9f4bd5cb91
--- /dev/null
+++ b/changelog.d/gbt-mintime.md
@@ -0,0 +1,7 @@
+Fixed
+
+- **`getblocktemplate` `mintime` is one past the tip's median time.** It was
+  the median itself, which a block cannot use (`time-too-old`). Core also
+  raises its minimum to the previous block's time minus 600 seconds at
+  retarget heights; that floor is not part of this fix. The Esplora
+  `GET /block-template` JSON follows.
diff --git a/crates/rbitcoin-rpc/src/methods/mine.rs b/crates/rbitcoin-rpc/src/methods/mine.rs
index 9811c3d053..393b1e8b81 100644
--- a/crates/rbitcoin-rpc/src/methods/mine.rs
+++ b/crates/rbitcoin-rpc/src/methods/mine.rs
@@ -645,11 +645,14 @@ pub fn gbt_template(ctx: &RpcContext) -> Result<Value, Value> {
         rbitcoin_query::expected_next_bits(ctx.query.as_ref(), &params, Height(next_h), curtime)
             .map(|c| c.to_consensus())
             .unwrap_or(tip_bits);
+    // The next block must be above the tip median. Core's `GetMinimumTime`
+    // also raises this at retarget heights; that floor is not applied here.
     let mintime = if tip_h == 0 {
         tip_time
     } else {
         rbitcoin_query::median_time_past(ctx.query.as_ref(), Height(tip_h)).unwrap_or(tip_time)
-    };
+    }
+    .saturating_add(1);
     let selected = mempool_block_txs(ctx);
     let mut fees = 0u64;
     let mut tx_json = Vec::with_capacity(selected.len());
diff --git a/crates/rbitcoin-rpc/src/methods_tests.rs b/crates/rbitcoin-rpc/src/methods_tests.rs
index a77e6f2803..068d02bab1 100644
--- a/crates/rbitcoin-rpc/src/methods_tests.rs
+++ b/crates/rbitcoin-rpc/src/methods_tests.rs
@@ -3893,6 +3893,24 @@ fn submitblock_store_fault_does_not_cache_block_invalid() {
     let _ = std::fs::remove_dir_all(&dir);
 }
 
+/// Core `GetMinimumTime`: `mintime` is the lowest time the next block can
+/// carry, one past the tip median. At genesis that median is its time.
+#[test]
+fn getblocktemplate_mintime_is_one_past_the_tip_median() {
+    let (ctx, dir, hub) = ctx_from_mature_pad(300_000_000);
+    let gbt = dispatch(&ctx, "getblocktemplate", vec![json!({"rules": ["segwit"]})]).unwrap();
+    let tip = Height(hub.tip_height().unwrap());
+    let mtp = rbitcoin_query::median_time_past(hub.query.as_ref(), tip).unwrap();
+    assert_eq!(gbt["mintime"], u64::from(mtp) + 1, "{gbt}");
+    let _ = std::fs::remove_dir_all(&dir);
+
+    let (ctx, dir, hub) = ctx_regtest_hub();
+    let gbt = dispatch(&ctx, "getblocktemplate", vec![json!({"rules": ["segwit"]})]).unwrap();
+    let genesis = hub.tip_header().unwrap().time;
+    assert_eq!(gbt["mintime"], u64::from(genesis) + 1, "{gbt}");
+    let _ = std::fs::remove_dir_all(&dir);
+}
+
 /// A sibling that spends the coin the current tip also spent is a competing
 /// block, not a permanent `duplicate-invalid`.
 #[test]