diff --git a/NEWS.md b/NEWS.md
index 1f589d30..57e24d28 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -4,6 +4,7 @@
   (PR #309)
 - Remove deprecated functions and arguments (PR #311, PR #313)
 - Minor cleanups and improvements (PR #313).
+- Add more tests to increase coverage (PR #315)
 
 # anndataR 0.2.0
 
diff --git a/inst/extdata/example.h5ad b/inst/extdata/example.h5ad
index 66b9c764..a009bfb8 100644
Binary files a/inst/extdata/example.h5ad and b/inst/extdata/example.h5ad differ
diff --git a/inst/scripts/example_h5ad.py b/inst/scripts/example_h5ad.py
index 0559c94b..9142caaf 100644
--- a/inst/scripts/example_h5ad.py
+++ b/inst/scripts/example_h5ad.py
@@ -1,9 +1,9 @@
-# python v3.10.10
-import anndata  # anndata v0.8.0
-import scanpy  # scanpy v1.9.3
-import numpy  # numpy v1.23.5
-import pandas  # pandas v2.0.0
-import scipy.sparse  # scipy v1.10.1
+# python v3.13.5
+import anndata  # anndata v0.11.4
+import scanpy  # scanpy v1.11.4
+import numpy  # numpy v2.2.6
+import pandas  # pandas v2.3.0
+import scipy.sparse  # scipy v1.14.1
 
 # This script uses Python to create an example H5AD file for testing
 # interoperability between languages. It is designed to be a small but
@@ -22,6 +22,9 @@
 #
 # CHANGELOG
 #
+# v0.3.0 (2025-08-04)
+# - Add adata.varp["test_varp"] to test reading of varp
+# - Update package versions to latest stable versions
 # v0.2.0 (2023-05-11)
 # - Add 1D sparse matrix to `adata.uns["Sparse1D"]
 # - Reduce the size of `adata.uns["String2D"]` and add columns to values
@@ -83,5 +86,8 @@
 scanpy.tl.leiden(adata)
 scanpy.tl.rank_genes_groups(adata, "leiden")
 
+# add varp to test reading of varp
+adata.varp["test_varp"] = numpy.random.rand(adata.n_vars, adata.n_vars)
+
 # Write the H5AD file
-adata.write("example.h5ad")
+adata.write_h5ad("inst/extdata/example.h5ad", compression="gzip")
diff --git a/tests/testthat/test-HDF5AnnData.R b/tests/testthat/test-HDF5AnnData.R
index eef20294..742cf024 100644
--- a/tests/testthat/test-HDF5AnnData.R
+++ b/tests/testthat/test-HDF5AnnData.R
@@ -50,6 +50,26 @@ test_that("reading varm works", {
   )
 })
 
+# trackstatus: class=HDF5AnnData, feature=test_get_obsp, status=done
+test_that("reading obsp works", {
+  obsp <- adata$obsp
+  expect_true(is.list(obsp), "list")
+  expect_equal(
+    names(obsp),
+    c("connectivities", "distances")
+  )
+})
+
+# trackstatus: class=HDF5AnnData, feature=test_get_varp, status=done
+test_that("reading varp works", {
+  varp <- adata$varp
+  expect_true(is.list(varp), "list")
+  expect_equal(
+    names(varp),
+    c("test_varp")
+  )
+})
+
 # trackstatus: class=HDF5AnnData, feature=test_get_obs, status=done
 test_that("reading obs works", {
   obs <- adata$obs
@@ -187,3 +207,71 @@ test_that("writing var names works", {
   h5ad$var_names <- LETTERS[1:20]
   expect_identical(h5ad$var_names, LETTERS[1:20])
 })
+
+# trackstatus: class=HDF5AnnData, feature=test_set_obsm, status=done
+test_that("writing obsm works", {
+  h5ad_file <- withr::local_tempfile(fileext = ".h5ad")
+  obs <- data.frame(row.names = 1:10)
+  var <- data.frame(row.names = 1:20)
+  h5ad <- HDF5AnnData$new(h5ad_file, obs = obs, var = var)
+
+  obsm_x <- matrix(rnorm(10 * 5), nrow = 10, ncol = 5)
+  h5ad$obsm <- list(X = obsm_x)
+  expect_identical(h5ad$obsm$X, obsm_x)
+})
+
+# trackstatus: class=HDF5AnnData, feature=test_set_varm, status=done
+test_that("writing varm works", {
+  h5ad_file <- withr::local_tempfile(fileext = ".h5ad")
+  obs <- data.frame(row.names = 1:10)
+  var <- data.frame(row.names = 1:20)
+  h5ad <- HDF5AnnData$new(h5ad_file, obs = obs, var = var)
+  varm_x <- matrix(rnorm(20 * 5), nrow = 20, ncol = 5)
+  h5ad$varm <- list(PCs = varm_x)
+  expect_identical(h5ad$varm$PCs, varm_x)
+})
+
+# trackstatus: class=HDF5AnnData, feature=test_set_obsp, status=done
+test_that("writing obsp works", {
+  h5ad_file <- withr::local_tempfile(fileext = ".h5ad")
+  obs <- data.frame(row.names = 1:10)
+  var <- data.frame(row.names = 1:20)
+  h5ad <- HDF5AnnData$new(h5ad_file, obs = obs, var = var)
+
+  obsp_x <- matrix(rnorm(10 * 10), nrow = 10, ncol = 10)
+  h5ad$obsp <- list(connectivities = obsp_x)
+  expect_identical(h5ad$obsp$connectivities, obsp_x)
+})
+
+# trackstatus: class=HDF5AnnData, feature=test_set_varp, status=done
+test_that("writing varp works", {
+  h5ad_file <- withr::local_tempfile(fileext = ".h5ad")
+  obs <- data.frame(row.names = 1:10)
+  var <- data.frame(row.names = 1:20)
+  h5ad <- HDF5AnnData$new(h5ad_file, obs = obs, var = var)
+
+  varp_x <- matrix(rnorm(20 * 20), nrow = 20, ncol = 20)
+  h5ad$varp <- list(connectivities = varp_x)
+  expect_identical(h5ad$varp$connectivities, varp_x)
+})
+
+# trackstatus: class=HDF5AnnData, feature=test_set_uns, status=done
+test_that("writing uns works", {
+  h5ad_file <- withr::local_tempfile(fileext = ".h5ad")
+  obs <- data.frame(row.names = 1:10)
+  var <- data.frame(row.names = 1:20)
+  h5ad <- HDF5AnnData$new(h5ad_file, obs = obs, var = var)
+
+  h5ad$uns <- list(
+    foo = "bar",
+    baz = c(1, 2, 3),
+    nested = list(
+      nested_foo = "nested_bar",
+      nested_baz = c(4L, 5L, 6L)
+    )
+  )
+  expect_identical(h5ad$uns$foo, "bar")
+  expect_equal(h5ad$uns$baz, c(1, 2, 3), ignore_attr = TRUE)
+  expect_identical(h5ad$uns$nested$nested_foo, "nested_bar")
+  expect_equal(h5ad$uns$nested$nested_baz, c(4L, 5L, 6L), ignore_attr = TRUE)
+})