diff --git a/chain/ethereum/src/data_source.rs b/chain/ethereum/src/data_source.rs
index 709884496e8..a56f06f4022 100644
--- a/chain/ethereum/src/data_source.rs
+++ b/chain/ethereum/src/data_source.rs
@@ -1302,6 +1302,10 @@ impl blockchain::DataSourceTemplate<Chain> for DataSourceTemplate {
     fn kind(&self) -> &str {
         &self.kind
     }
+
+    fn has_address_scoped_block_handler(&self) -> bool {
+        self.mapping.has_block_handler_with_call_filter()
+    }
 }
 
 #[derive(Clone, Debug, Default, Eq, PartialEq, Deserialize)]
@@ -1597,3 +1601,82 @@ fn string_to_b256(s: &str) -> B256 {
 pub struct TemplateSource {
     pub abi: String,
 }
+
+#[cfg(test)]
+mod address_scoped_block_handler_tests {
+    use super::*;
+    use graph::blockchain::DataSourceTemplate as _;
+
+    fn template_with(block_handlers: Vec<MappingBlockHandler>) -> DataSourceTemplate {
+        let mut mapping = Mapping {
+            kind: "ethereum/events".to_string(),
+            api_version: semver::Version::new(0, 0, 7),
+            language: "wasm/assemblyscript".to_string(),
+            entities: vec![],
+            abis: vec![],
+            block_handlers,
+            call_handlers: vec![],
+            event_handlers: vec![],
+            runtime: std::sync::Arc::new(vec![]),
+            link: Link {
+                link: "test".to_string(),
+            },
+        };
+        mapping.block_handlers.shrink_to_fit();
+        DataSourceTemplate {
+            kind: "ethereum/contract".to_string(),
+            network: Some("test".to_string()),
+            name: "T".to_string(),
+            manifest_idx: 0,
+            source: TemplateSource {
+                abi: "abi".to_string(),
+            },
+            mapping,
+        }
+    }
+
+    fn handler(filter: Option<BlockHandlerFilter>) -> MappingBlockHandler {
+        MappingBlockHandler {
+            handler: "h".to_string(),
+            filter,
+        }
+    }
+
+    #[test]
+    fn call_filtered_block_handler_is_address_scoped() {
+        let template = template_with(vec![handler(Some(BlockHandlerFilter::Call))]);
+        assert!(template.has_address_scoped_block_handler());
+    }
+
+    #[test]
+    fn block_handlers_without_a_call_filter_are_not_address_scoped() {
+        for filter in [
+            None,
+            Some(BlockHandlerFilter::Once),
+            Some(BlockHandlerFilter::Polling {
+                every: std::num::NonZeroU32::new(1).unwrap(),
+            }),
+        ] {
+            let template = template_with(vec![handler(filter.clone())]);
+            assert!(
+                !template.has_address_scoped_block_handler(),
+                "a {filter:?} block handler does not depend on the created address"
+            );
+        }
+    }
+
+    #[test]
+    fn a_template_without_block_handlers_is_not_address_scoped() {
+        assert!(!template_with(vec![]).has_address_scoped_block_handler());
+    }
+
+    #[test]
+    fn one_call_filtered_handler_is_enough_among_other_handlers() {
+        let template = template_with(vec![
+            handler(None),
+            handler(Some(BlockHandlerFilter::Call)),
+            handler(Some(BlockHandlerFilter::Once)),
+        ]);
+        assert!(template.has_address_scoped_block_handler());
+    }
+}
diff --git a/core/src/subgraph/runner/mod.rs b/core/src/subgraph/runner/mod.rs
index 026be3dfc27..e39a4b4a7b6 100644
--- a/core/src/subgraph/runner/mod.rs
+++ b/core/src/subgraph/runner/mod.rs
@@ -14,8 +14,8 @@ use graph::blockchain::block_stream::{
     BlockStream, BlockStreamEvent, BlockWithTriggers, FirehoseCursor,
 };
 use graph::blockchain::{
-    Block, BlockTime, Blockchain, DataSource as _, SubgraphFilter, Trigger, TriggerFilter as _,
-    TriggerFilterWrapper,
+    Block, BlockTime, Blockchain, DataSource as _, DataSourceTemplate as _, SubgraphFilter,
+    Trigger, TriggerFilter as _, TriggerFilterWrapper,
 };
 use graph::components::store::{
     EmptyStore, GetScope, ReadStore, SeqGenerator, StoredDynamicDataSource,
@@ -147,7 +147,32 @@ where
     }
 
     fn is_static_filters_enabled(&self) -> bool {
-        self.inputs.static_filters || self.ctx.hosts_len() > ENV_VARS.static_filters_threshold
+        let requested =
+            self.inputs.static_filters || self.ctx.hosts_len() > ENV_VARS.static_filters_threshold;
+        if !requested {
+            return false;
+        }
+
+        // Static filters deliberately drop the addresses of created data
+        // sources, so a template handler that fires only on calls to the
+        // address of the data source it creates has nothing to match on and
+        // would never run. Such subgraphs have to keep the full filter, which
+        // means restarting the block stream whenever a data source is created.
+        let incompatible = self.ctx.templates().iter().any(|template| {
+            template
+                .as_onchain()
+                .is_some_and(|t| t.has_address_scoped_block_handler())
+        });
+        if incompatible {
+            info!(
+                self.logger,
+                "subgraph has a template handler that only fires on calls to the created \
+                 data source's address; keeping the full trigger filter instead of static filters"
+            );
+            return false;
+        }
+
+        true
     }
 
     fn build_filter(&self) -> TriggerFilterWrapper<C> {
diff --git a/graph/src/blockchain/mod.rs b/graph/src/blockchain/mod.rs
index df942d19910..4829f7c3583 100644
--- a/graph/src/blockchain/mod.rs
+++ b/graph/src/blockchain/mod.rs
@@ -380,6 +380,18 @@ pub trait DataSourceTemplate<C: Blockchain>: Send + Sync + Debug {
     fn name(&self) -> &str;
     fn manifest_idx(&self) -> u32;
     fn kind(&self) -> &str;
+    /// Whether a data source created from this template carries a handler that
+    /// only fires on calls to that specific data source's address, and which
+    /// therefore cannot be expressed by a filter built from the static data
+    /// sources alone.
+    ///
+    /// Static filters drop the addresses of created data sources on purpose, so
+    /// a chain that can have such a handler must report it here and let the
+    /// runner fall back to the full filter. Defaults to `false` for chains
+    /// whose trigger filters have no equivalent construct.
+    fn has_address_scoped_block_handler(&self) -> bool {
+        false
+    }
     fn info(&self) -> DataSourceTemplateInfo {
         DataSourceTemplateInfo {
             api_version: self.api_version(),