diff --git a/crates/eps/src/import/data.rs b/crates/eps/src/import/data.rs
index 9c3144e02..aa10998e9 100644
--- a/crates/eps/src/import/data.rs
+++ b/crates/eps/src/import/data.rs
@@ -1093,6 +1093,11 @@ impl Interp<'_> {
         let row = row_bits.div_ceil(8);
         // Several sources are read in turn, a row at a time each (zeros past their ends).
         let sources = if multi { &s.sources[..] } else { s.sources.get(..1).ok_or(PsError::Ps("undefined", "DataSource".into()))? };
+        if sources.len() > n {
+            return ps_err("rangecheck", "DataSource");
+        }
+        let plane = row.checked_mul(s.h).filter(|p| *p <= MAX_DATA).ok_or(PsError::Limit("decoded data is too large"))?;
+        self.alloc(plane.saturating_mul(sources.len()))?;
         let mut planes = self.read_sources(sources, row * s.h, if multi { row } else { row * s.h })?;
         for p in &mut planes {
             p.resize(row * s.h, 0);
diff --git a/crates/eps/src/import/tests.rs b/crates/eps/src/import/tests.rs
index 99dcee8bd..bc24e0b66 100644
--- a/crates/eps/src/import/tests.rs
+++ b/crates/eps/src/import/tests.rs
@@ -1131,3 +1131,34 @@ fn search_in_a_loop_runs_out_of_the_budget() {
     let make = "/h 4194304 string def /n 2097152 string def n 2097152 1 sub 1 put";
     runs_out_of_budget(&format!("{make} {{ h n search {{ pop pop pop }} {{ pop }} ifelse }} loop"));
 }
+
+/// #3568: an image dictionary with more data sources than colour components is a `rangecheck`.
+#[test]
+fn an_image_with_more_data_sources_than_components_is_refused() {
+    let sources = "<80> ".repeat(64);
+    let e = import(&eps(&format!(
+        "/DeviceGray setcolorspace << /ImageType 1 /Width 64 /Height 64 /BitsPerComponent 8 /MultipleDataSources true \
+         /ImageMatrix [64 0 0 64 0 0] /DataSource [{sources}] >> image"
+    )))
+    .unwrap_err();
+    assert!(e.contains("rangecheck") && e.contains("DataSource"), "{e}");
+}
+
+/// #3568: every data source's plane is charged against the memory budget, not only the RGBA
+/// output: two large four-source images together go over it.
+#[test]
+fn the_planes_of_multi_source_images_are_charged() {
+    let image = "/DeviceCMYK setcolorspace << /ImageType 1 /Width 8192 /Height 8192 /BitsPerComponent 8 \
+                 /MultipleDataSources true /ImageMatrix [8192 0 0 8192 0 0] /DataSource [<80> <80> <80> <80>] >> image\n";
+    let r = import(&eps(&image.repeat(2))).unwrap();
+    assert!(r.warnings.iter().any(|w| w.contains("too much memory")), "{:?}", r.warnings);
+}
+
+/// #3568: a single sample plane over the data limit is refused.
+#[test]
+fn an_oversized_image_plane_is_refused() {
+    let e = import(&eps("/DeviceCMYK setcolorspace << /ImageType 1 /Width 8192 /Height 8192 /BitsPerComponent 16 \
+         /ImageMatrix [8192 0 0 8192 0 0] /DataSource <80> >> image"))
+    .unwrap_err();
+    assert!(e.contains("too large"), "{e}");
+}